Take this Quiz: Calculus AB — the differentiation rules | Zestly

Question 1

Let $h(x) = x^2 	an(x)$. What is $h'(x)$?

Accepted Answer

$2x	an(x) + x^2\sec^2(x)$

Answer

$2x	an(x) + x^2\sec(x)	an(x)$

Answer

$2x\sec^2(x)$

Answer

$2x	an(x) - x^2\sec^2(x)$

Question 2

Find the derivative of $f(x) = \frac{x^3}{x^2 + 1}$.

Accepted Answer

$\frac{x^4 + 3x^2}{(x^2 + 1)^2}$

Answer

$\frac{x^4 - 3x^2}{(x^2 + 1)^2}$

Answer

$\frac{3x^2(x^2 + 1) - x^3(2x)}{x^2 + 1}$

Answer

$\frac{3x^2}{2x}$

Question 3

Find the derivative of $h(x) = \sin^3(x^2)$.

Accepted Answer

$6x \sin^2(x^2) \cos(x^2)$

Answer

$3\sin^2(x^2) \cos(x^2)$

Answer

$2x \cos(x^2)$

Answer

$3\sin^2(x^2)$

Question 4

Find the derivative of $f(x) = \cos(x^3 + 2x)$.

Answer

$-\sin(x^3 + 2x)$

Answer

$\sin(x^3 + 2x)(3x^2 + 2)$

Answer

$\cos(3x^2 + 2)$

Answer

$-\sin(x^3 + 2x)(3x^2 + 2)$

Question 5

Find the derivative of $f(x) = 5^{x^2}$.

Answer

$x^2 \cdot 5^{x^2-1}$

Answer

$5^{x^2} \cdot \ln(x^2) \cdot 2x$

Answer

$5^{x^2} \cdot \ln(5) \cdot 2x$

Answer

$5^{x^2} \cdot 2x$