Тренировочный тест по производным (степенная, произведение, цепочка)

Question 1

Найдите $\frac{d}{dx}\left(5x^{-3}\right)$.

Accepted Answer

$-15x^{-4}$

Answer

$15x^{-4}$

Answer

$-3x^{-4}$

Answer

$-15x^{-2}$

Question 2

Найдите $\frac{d}{dx}\left(\sin(x^2)\right)$.

Accepted Answer

$2x\cos(x^2)$

Answer

$\cos(2x)$

Answer

$\cos(x^2)$

Answer

$2\cos(x^2)$

Question 3

Найдите производную $y=\ln\left(\frac{x^2+1}{x}\right)$.

Accepted Answer

$\frac{2x}{x^2+1}-\frac{1}{x}$

Answer

$\frac{2}{x^2+1}-\frac{1}{x}$

Answer

$\frac{2x}{x^2+1}\cdot \frac{1}{x}$

Answer

$\frac{2x-1}{x^2+1}$

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