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192 x^{2} {(2 x^{2} + 5)}^{2} + 16 {(2 x^{2} + 5)}^{3}

192 x^{2} \left(2 x^{2} + 5\right)^{2}+16 \left(2 x^{2} + 5\right)^{3}

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Expanding de derivative voor multiplication.

$\frac{d}{d x} [4 {(2 x^{2} + 5)}^{3} \times (4 x)] = \frac{d}{d x} [4] \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times \frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x]$

Expanding de derivative voor multiplication.

Multiplication can zijn grouped differently, but de resultaat remains de same.

$\frac{d}{d x} [4 {(2 x^{2} + 5)}^{3} \times (4 x)] = \frac{d}{d x} [4 \times ({(2 x^{2} + 5)}^{3} \times (4 x))]$

Applying de product rule van derivatives.

$\frac{d}{d x} [4 \times ({(2 x^{2} + 5)}^{3} \times (4 x))] = \frac{d}{d x} [4] \times ({(2 x^{2} + 5)}^{3} \times (4 x)) + 4 \times \frac{d}{d x} [{(2 x^{2} + 5)}^{3} \times (4 x)]$

Expanding de derivative voor multiplication.

Applying de product rule van derivatives.

$\frac{d}{d x} [{(2 x^{2} + 5)}^{3} \times (4 x)] = \frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x]$

Multiplication can zijn grouped differently, but de resultaat remains de same.

$\frac{d}{d x} [4] \times ({(2 x^{2} + 5)}^{3} \times (4 x)) + 4 (\frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x]) = \frac{d}{d x} [4] \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 (\frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x])$

Multiplying een getal door een Som of difference van two getallen can zijn done door multiplying each getal individually en dan adding of subtracting de resultaten.

$\frac{d}{d x} [4] \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 (\frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x]) = \frac{d}{d x} [4] \times {(2 x^{2} + 5)}^{3} \times (4 x) + (4 \times (\frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x)) + 4 \times ({(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x]))$

Multiplication can zijn grouped differently, but de resultaat remains de same.

$\frac{d}{d x} [4] \times {(2 x^{2} + 5)}^{3} \times (4 x) + (4 \times (\frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x)) + 4 \times ({(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x])) = \frac{d}{d x} [4] \times {(2 x^{2} + 5)}^{3} \times (4 x) + (4 \times \frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x]))$

Multiplication can zijn grouped differently, but de resultaat remains de same.

$\frac{d}{d x} [4] \times {(2 x^{2} + 5)}^{3} \times (4 x) + (4 \times \frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x])) = \frac{d}{d x} [4] \times {(2 x^{2} + 5)}^{3} \times (4 x) + (4 \times \frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x])$

Addition can zijn grouped differently, but de resultaat remains de same.

$\frac{d}{d x} [4] \times {(2 x^{2} + 5)}^{3} \times (4 x) + (4 \times \frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x]) = \frac{d}{d x} [4] \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times \frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x]$

De derivative van een constant waarde is always zero.

$\frac{d}{d x} [4] \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times \frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x] = 0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times \frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x]$

Computing de derivative van een macht function.

$0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times \frac{d}{d x} [{(2 x^{2} + 5)}^{3}] \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x] = 0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x]$

Applying de product rule van derivatives.

$0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times \frac{d}{d x} [4 x] = 0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} (\frac{d}{d x} [4] \times x + 4 \times \frac{d}{d x} [x])$

De derivative van een constant waarde is always zero.

$0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} (\frac{d}{d x} [4] \times x + 4 \times \frac{d}{d x} [x]) = 0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} (0 x + 4 \times \frac{d}{d x} [x])$

Multiplying een getal door zero always resultaten in zero.

$0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} (0 x + 4 \times \frac{d}{d x} [x]) = 0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} (0 + 4 \times \frac{d}{d x} [x])$

Adding zero naar een getal, which does Neet change its waarde.

$0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} (0 + 4 \times \frac{d}{d x} [x]) = 0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times (4 \times \frac{d}{d x} [x])$

De derivative van een variable met respect naar itself is always equal naar one.

$0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times (4 \times \frac{d}{d x} [x]) = 0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times (4 \times 1)$

Multiplying een getal door one, which does Neet change its waarde.

$0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times (4 \times 1) = 0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

De derivative van een constant waarde is always zero.

$0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (\frac{d}{d x} [3] \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4 = 0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

Applying de Som rule van derivatives.

$0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times \frac{d}{d x} [2 x^{2} + 5])) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4 = 0 {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times (\frac{d}{d x} [2 x^{2}] + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

Multiplying een getal door zero always resultaten in zero.

$0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 \times \ln (2 x^{2} + 5) + \frac{3}{2 x^{2} + 5} \times (\frac{d}{d x} [2 x^{2}] + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4 = 0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times (\frac{d}{d x} [2 x^{2}] + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

Applying de product rule van derivatives.

$0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times (\frac{d}{d x} [2 x^{2}] + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4 = 0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times ((\frac{d}{d x} [2] \times x^{2} + 2 \times \frac{d}{d x} [x^{2}]) + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

De derivative van een constant waarde is always zero.

$0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times ((\frac{d}{d x} [2] \times x^{2} + 2 \times \frac{d}{d x} [x^{2}]) + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4 = 0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times ((0 x^{2} + 2 \times \frac{d}{d x} [x^{2}]) + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

Multiplying een getal door zero always resultaten in zero.

$0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times ((0 x^{2} + 2 \times \frac{d}{d x} [x^{2}]) + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4 = 0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times ((0 + 2 \times \frac{d}{d x} [x^{2}]) + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

Adding zero naar een getal, which does Neet change its waarde.

$0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times ((0 + 2 \times \frac{d}{d x} [x^{2}]) + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4 = 0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times (2 \times \frac{d}{d x} [x^{2}] + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

Computing de derivative van x raised naar de macht van n.

$0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times (2 \times \frac{d}{d x} [x^{2}] + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4 = 0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times (2 \times (2 x^{2 - 1}) + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

Subtracting one van een getal.

$0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times (2 \times (2 x^{2 - 1}) + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4 = 0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times (2 \times (2 x^{1}) + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

Multiplication can zijn grouped differently, but de resultaat remains de same.

$0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times (2 \times (2 x^{1}) + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4 = 0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times ((2 \times 2) \times x^{1} + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

Multiplying two geheel getals together.

$0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times ((2 \times 2) \times x^{1} + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4 = 0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times (4 x^{1} + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

De derivative van een constant waarde is always zero.

$0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times (4 x^{1} + \frac{d}{d x} [5]))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4 = 0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} (0 + \frac{3}{2 x^{2} + 5} \times (4 x^{1} + 0))) \times (4 x) + 4 {(2 x^{2} + 5)}^{3} \times 4$

Adding zero naar een getal, which does Neet change its waarde.

$0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} \times (0 + \frac{3}{2 x^{2} + 5} \times (4 x^{1} + 0))) \times (4 x) + 4 \times {(2 x^{2} + 5)}^{3} \times 4 = 0 \times {(2 x^{2} + 5)}^{3} \times (4 x) + 4 \times ({(2 x^{2} + 5)}^{3} \times (\frac{3}{2 x^{2} + 5} \times (4 x^{1} + 0))) \times (4 x) + 4 \times {(2 x^{2} + 5)}^{3} \times 4$