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Řešení - Derivative

2 x + 3

2x+3

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1. Krok 160: upravte derivaci

4 additional steps

Expanding the derivative for addition.

$\frac{d}{d x} [x^{2} + 3 x + 34] = \frac{d}{d x} [x^{2}] + \frac{d}{d x} [3 x] + \frac{d}{d x} [34]$

Expanding the derivative for addition.

$\frac{d}{d x} [x^{2} + 3 x + 34] = \frac{d}{d x} [x^{2}] + \frac{d}{d x} [3 x] + \frac{d}{d x} [34]$

Addition can be grouped differently, but the result remains the same.

$\frac{d}{d x} [x^{2} + 3 x + 34] = \frac{d}{d x} [x^{2} + (3 x + 34)]$

Applying the sum rule of derivatives.

$\frac{d}{d x} [x^{2} + (3 x + 34)] = \frac{d}{d x} [x^{2}] + \frac{d}{d x} [3 x + 34]$

Applying the sum rule of derivatives.

$\frac{d}{d x} [x^{2}] + \frac{d}{d x} [3 x + 34] = \frac{d}{d x} [x^{2}] + (\frac{d}{d x} [3 x] + \frac{d}{d x} [34])$

Addition can be grouped differently, but the result remains the same.

$\frac{d}{d x} [x^{2}] + (\frac{d}{d x} [3 x] + \frac{d}{d x} [34]) = \frac{d}{d x} [x^{2}] + \frac{d}{d x} [3 x] + \frac{d}{d x} [34]$

Computing the derivative of x raised to the power of n.

$\frac{d}{d x} [x^{2}] + \frac{d}{d x} [3 x] + \frac{d}{d x} [34] = 2 x^{2 - 1} + \frac{d}{d x} [3 x] + \frac{d}{d x} [34]$

Subtracting one from a number.

$2 x^{2 - 1} + \frac{d}{d x} [3 x] + \frac{d}{d x} [34] = 2 x^{1} + \frac{d}{d x} [3 x] + \frac{d}{d x} [34]$

Any number raised to the power of one equals the number itself.

$2 x^{1} + \frac{d}{d x} [3 x] + \frac{d}{d x} [34] = 2 x + \frac{d}{d x} [3 x] + \frac{d}{d x} [34]$

Applying the product rule of derivatives.

$2 x + \frac{d}{d x} [3 x] + \frac{d}{d x} [34] = 2 x + (\frac{d}{d x} [3] \times x + 3 \times \frac{d}{d x} [x]) + \frac{d}{d x} [34]$

The derivative of a constant value is always zero.

$2 x + (\frac{d}{d x} [3] \times x + 3 \times \frac{d}{d x} [x]) + \frac{d}{d x} [34] = 2 x + (0 x + 3 \times \frac{d}{d x} [x]) + \frac{d}{d x} [34]$

Multiplying a number by zero always results in zero.

$2 x + (0 x + 3 \times \frac{d}{d x} [x]) + \frac{d}{d x} [34] = 2 x + (0 + 3 \times \frac{d}{d x} [x]) + \frac{d}{d x} [34]$

Adding zero to a number, which does not change its value.

$2 x + (0 + 3 \times \frac{d}{d x} [x]) + \frac{d}{d x} [34] = 2 x + 3 \times \frac{d}{d x} [x] + \frac{d}{d x} [34]$

The derivative of a variable with respect to itself is always equal to one.

$2 x + 3 \times \frac{d}{d x} [x] + \frac{d}{d x} [34] = 2 x + 3 \times 1 + \frac{d}{d x} [34]$

Multiplying a number by one, which does not change its value.

$2 x + 3 \times 1 + \frac{d}{d x} [34] = 2 x + 3 + \frac{d}{d x} [34]$

The derivative of a constant value is always zero.

$2 x + 3 + \frac{d}{d x} [34] = 2 x + 3 + 0$

Adding zero to a number, which does not change its value.

$2 x + 3 + 0 = 2 x + 3$

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Derivace je klíčová pro pochopení rychlosti změny, extrémů a tvaru grafu funkcí.

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Derivative

Řešení - Derivative

Vysvětlení krok za krokem

1. Krok 160: upravte derivaci

Proč se to učit

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