Question 1

A function is defined by $g(x)=(6x^2+3)^{10}$.  Find $g'(x)$.

Accepted Answer

$120x(6x^2+3)^9$

Answer

$6x(6x^2+3)^9$

Answer

$10(6x^2+3)^9$

Answer

$(12x)^{10}$

Question 2

If $y = 6(4x+2)^4$, then find $y'$.

Accepted Answer

$96(4x+2)^3$

Answer

$4x^3$

Answer

$(4x+2)^3$

Answer

$96(4x-2)^3$

Question 3

If a function is defined by $y=-5(5x^2+5)^4$, then find the expression for $y'$.

Accepted Answer

$-200x(5x^2+5)^3$

Answer

$(5x^2+5)^3$

Answer

$x(5x^2+5)^3$

Answer

$(5x^2)^3$

Question 4

If $f(x)=4\sqrt{4x+3}$, then find $f'(x)$.

Accepted Answer

$\frac{8}{\sqrt{4x+3}}$

Answer

$\frac{1}{\sqrt{x+3}}$

Answer

$\frac{4}{\sqrt{4x+3}}$

Answer

$\frac{1}{\sqrt{4x+3}}$

Question 5

A function is given by $f(x)=\sqrt{8x-3}$.  What is $f'(x)$?

Accepted Answer

$\frac{4}{\sqrt{8x-3}}$

Answer

$-\sqrt{8x-3}$

Answer

$\frac{1}{\sqrt{8x-3}}$

Answer

$\frac{x}{2}$

Question 6

A function is defined by $f(x)=\sqrt[3]{5x^2+8}$, then $f'(x)=$?

Accepted Answer

$(\frac{10x}{3})(5x^2+8)^{-\frac{2}{3}}$

Answer

$(\frac{1}{3})(5x^2+8)^{-\frac{2}{3}}$

Answer

$5x(5x^2+8)^{-\frac{2}{3}}$

Answer

$(\frac{10x}{3})(5x^2+8)^{\frac{4}{3}}$

Question 7

If $y=\frac{5}{(x-2)^2}$, then find $y'$.

Accepted Answer

$-\frac{10}{(x-2)^3}$

Answer

$\frac{10}{(x-2)^3}$

Answer

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

Answer

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

Question 8

A function is defined by $h(x) = (5x^3+7x^2+3)^3$, then find $h'(x)$.

Accepted Answer

$(45x^2+42x)(5x^3+7x^2+3)^2$

Answer

$(45x^2+42x)(5x^3)$

Answer

$(42x)(5x^3+7x^2+3)^2$

Answer

$(45x^2+42x)$

Question 9

If $y=9x^{27}+2x^{26}$, then find $y'$.

Accepted Answer

$243x^{26}+52x^{25}$

Answer

$243x^{26}-x^{25}$

Answer

$243x^{26}+x^{25}$

Answer

$x^{26}+52x^{25}$

Question 10

If $y=(8x^2+6x)^2$, then what is $y'$?

Accepted Answer

$256x^3+288x^2+72x$

Answer

$x^3+288x^2+72x$

Answer

$256x^3+288x^2$

Answer

$256x^3-72x$

Question 11

If $y=(6x^3-6x^2)^2$, then $y'$ is ?

Accepted Answer

$216x^5-360x^4+144x^3$

Answer

$x^5-360x^4+148$

Answer

$216x^5-360x^4+147$

Answer

$216x^5+144x^3+145x^2$

Question 12

If $y=(8x+5)^3$, then $y'$ is ?

Accepted Answer

$24(8x+5)^2$

Answer

$8x^2$

Answer

$-(8x-5)^2$

Answer

$(8x+5)^2$

Question 13

Given the function $y=-8\sqrt{(5x^2+8x)^3}$, then what is $y'$?

Accepted Answer

$-(120x+96)\sqrt{5x^2+8x}$

Answer

$-\sqrt{5x^2-8x}-10x^2$

Answer

$-(120x+96)$

Answer

$\sqrt{5x^2-8x}+10x$

Question 14

If $y=-5\sqrt{2x^2+9x}$, then $y'=$ ?

Accepted Answer

$-\frac{5}{2}$$\frac{4x+9}{\sqrt{2x^2+9x}}$

Answer

$\frac{4x+9}{\sqrt{2x^2+9x}}$

Answer

$\frac{9}{\sqrt{2x^2+9x}}$

Answer

$\frac{4x-9}{\sqrt{2x^2+9x}}$

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