Zadejte rovnici nebo úlohu

Vstup z kamery nebyl rozpoznán!

Řešení - Derivative

2 x + 1

2x+1

Vysvětlení krok za krokem

Expanding the derivative for addition.

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

Expanding the derivative for addition.

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

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

$\frac{d}{d x} [x^{2} + x + 1] = \frac{d}{d x} [x^{2} + (x + 1)]$

Applying the sum rule of derivatives.

$\frac{d}{d x} [x^{2} + (x + 1)] = \frac{d}{d x} [x^{2}] + \frac{d}{d x} [x + 1]$

Applying the sum rule of derivatives.

$\frac{d}{d x} [x^{2}] + \frac{d}{d x} [x + 1] = \frac{d}{d x} [x^{2}] + (\frac{d}{d x} [x] + \frac{d}{d x} [1])$

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

$\frac{d}{d x} [x^{2}] + (\frac{d}{d x} [x] + \frac{d}{d x} [1]) = \frac{d}{d x} [x^{2}] + \frac{d}{d x} [x] + \frac{d}{d x} [1]$

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

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

Subtracting one from a number.

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

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

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

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

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

The derivative of a constant value is always zero.

$2 x + 1 + \frac{d}{d x} [1] = 2 x + 1 + 0$

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

$2 x + 1 + 0 = 2 x + 1$

Bylo toto vysvětlení užitečné?

How did we do?

Learn more with Tiger

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