Question 1

If $y=(\sqrt{x}+8)\sqrt{\sqrt{x}-9}$, then what is $y'$?

Accepted Answer

$\frac{3x^{\frac{1}{2}}-10}{4x^{\frac{1}{2}} (x^{\frac{1}{2}}-9)^{\frac{1}{2}} }$

Answer

$\frac{x^{\frac{1}{2}}-10}{x^{\frac{1}{2}}(x^{\frac{1}{2}}-9)^{\frac{1}{2}}}$

Answer

None of the above

Answer

$\frac{10}{4x^{\frac{1}{2}} (x^{\frac{1}{2}}-9)^{\frac{1}{2}} }$

Question 2

If $f(x)=(3x^2+2x+2)^{50}$, then find $f'(0)$.

Accepted Answer

$100(2)^{49}$

Answer

$(2)^{48}$

Answer

$(2)^{49}$

Answer

$100(2)^{48}$

Question 3

If the cost function of a certain item is defined by $C(x)=200+\sqrt{50+2x^2}$, then find the marginal cost function.  (The derivative of the cost function.)

Accepted Answer

$\frac{2x}{\sqrt{50+2x^2}}$

Answer

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

Answer

$\frac{2}{\sqrt{5+x^2}}$

Answer

$\frac{x}{\sqrt{50+2x^2}}$

Question 4

If $R(x)=30\sqrt{800x-6x^2}$, then evaluate $R'(3)$.

Accepted Answer

236.6

Answer

238.6

Answer

237.6

Answer

235.6

Question 5

Find $f'(2)$ if $f(x)=3x^{101}$.

Accepted Answer

$303(2)^{100}$

Answer

$305(2)^{101}$

Answer

$306(2)^{99}$

Answer

$304(2)^{100}$

Question 6

If $F(t)=50-\frac{70}{\sqrt{7+t^2}}$, then $F'(t) = $______

Accepted Answer

$\frac{70t}{(7+t^2)^{\frac{3}{2}}}$

Answer

$\frac{7}{(7-t^2)^{\frac{3}{2}}}$

Answer

$\frac{t}{(7+t^2)^{\frac{3}{2}}}$

Answer

$\frac{70t}{(7t)^{\frac{3}{2}}}$

Question 7

If $f(x)=(x-7)^2+(3x^2+x^3)^5$, then $f'(x) = $?

Accepted Answer

$2x-14+5x(3x^2+x^3)^4(6+3x)$

Answer

$2x-14$

Answer

$5x(3x^2+x^3)^4$

Answer

$5x(3x^2+x^3)^4(6+3x)$

Question 8

A function is defined by $g(x)=(9x^2+2)^{10}$.  Evaluate $g'(2)$.

Accepted Answer

$360(38)^9$

Answer

$362(38)^8$

Answer

$361(38)^10$

Answer

$360(38)^7$

Question 9

If $h(x)=(4x^3+6x^2+5)^2$, then find the value of $h'(5)$.

Accepted Answer

$471,600$

Answer

$471,602$

Answer

$471,603$

Answer

$471,601$

Question 10

If $y=-4\sqrt{2x^2+8x}$, then evaluate $y'(1)$.

Accepted Answer

$-\frac{24}{\sqrt{10}}$

Answer

$\frac{12}{\sqrt{10}}$

Answer

$-\frac{1}{\sqrt{10}}$

Answer

$\frac{1}{\sqrt{10}}$

Question 11

Find $y'(5)$ if $y=3x^9$.

Accepted Answer

$27(5)^{8}$

Answer

$(5)^{8}$

Answer

$29(5)^{7}$

Answer

$28(5)^{8}$

Question 12

$\frac{d}{dx}(4\sqrt{x}-\frac{5}{\sqrt{x}})=$

Accepted Answer

$\frac{2}{\sqrt{x}}+\frac{5}{2x\sqrt{x}}$

Answer

$\frac{5}{2x\sqrt{x}}$

Answer

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

Answer

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

Question 13

$\frac{d}{dx}(4x+\frac{3}{x})^3=$

Accepted Answer

$144+192x^2-\frac{108}{x^2}-\frac{81}{x^4}$

Answer

$147-192x^2-\frac{108}{x^2}-\frac{81}{x^4}$

Answer

$145+1923x^2+\frac{108}{x^2}-\frac{81}{x^4}$

Answer

$146+192x^2+\frac{108}{x^2}+\frac{81}{x^4}$

Question 14

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

Accepted Answer

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

Answer

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

Answer

None of the above.

Answer

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

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