AP Calc AB Review for Test 09-12

Find the derivative of  $y=5x^2e^{3x}$ .

•  $y'=10xe^{3x}\left(2x+3\right)$ 

•  $y'=5xe^{3x}\left(3x+2\right)$ 

•  $y'=10ex^{3x}\left(3x+2\right)$ 

•  $y'=5xe^{3x}\left(2x+3\right)$  

Find the derivative of the following:  $\ln\left(3x^2-5x\right)$  

•  $\frac{6x-5}{3x^2-5x}$ 

•  $6x-5$ 

•  $\frac{x^3}{3}-\frac{5x^2}{2}$ 

•  $\frac{6x-5}{3x^3-2x}$ 

Differentiate:  $y=4\sin\left(3x\right)$ 

•  $y'=12\cos\left(3x\right)$  

•  $y'=4\cos\left(3x\right)$  

•  $y'=12\cos x$  

•  $y'=12\tan x$  

Given f (x) = 5sinx + 3x³cosx, f '(x) =

• -5cosx − 3x³sinx + 9x²cosx

• 5sinx − 3x³sinx + 9x²cosx

• 5cosx + 9x²cosx − 3x³sinx

• 5cosx + 3x³sinx + 9x²cosx

Find the derivative:
 $y=3\ln\left(x^2-3\right)$ 

•  $\frac{3}{x^2-3}$ 

•  $\frac{3x}{x^2-3}$ 

•  $\frac{6x}{x^2-3}$ 

•  $\frac{9x}{x^2-3}$  

Find the derivative of  $f\left(t\right)=\left(t^2+2t\right)^5$ 

•  $f'\left(t\right)=5\left(2t^{ }+2\right)^4$  

•  $f'\left(t\right)=5\left(t^2+2t\right)^4$ 

•  $f'\left(t\right)=5\left(t^2+2t\right)^4\left(2t\right)$ 

•  $f'\left(t\right)=5\left(t^2+2t\right)^4\left(2t+2\right)$ 

Find the derivative:
 $y=e^{\left(5x+\ln x\right)}$ 

•  $e^{\left(5+\frac{1}{x}\right)}$  

•  $e^{\left(5x+\ln x\right)}$  

•  $\left(5+\frac{1}{x}\right)e^{\left(5x+\ln x\right)}$ 

•  $\frac{5}{x}e^{\left(5x+\ln x\right)}$  

Find the second derivative of  $f\left(x\right)=x^2+e^x-\cos x$ 

•  $f''\left(x\right)=2+e^x+\cos x$ 

•  $f''\left(x\right)=2x+e^x+\cos x$ 

•  $f''\left(x\right)=2x+xe^x-\cos x$ 

•  $f''\left(x\right)=2x+e^x+\sin x$ 

• $\frac{1}{2}$

• $-\frac{1}{2}$

• $0$

• $\frac{3}{2}$

Find  $\frac{dy}{dx}$ if  $2xy^3-x^2y=2$ 

•  $\frac{dy}{dx}=2xy-2y^3$  

•  $\frac{dy}{dx}=\frac{2y\left(x-y^2\right)}{x\left(6y^2-x\right)}$  

•  $\frac{dy}{dx}=-\frac{2y}{x}$  

•  $\frac{dy}{dx}=2$