AP Calculus AB Final Exam Review Part 3

 $f\left(x\right)=\sin x$  Find the slope of the tangent line to f(x) at  $x=\frac{\pi}{6}$  

•  $\frac{1}{2}$  

•  $\frac{\sqrt{3}}{2}$  

•  $\frac{-\sqrt{3}}{2}$  

•  $\frac{-1}{2}$  

Tags

CCSS.HSF.TF.A.4

Find the derivative f(x) = tanxcosx

• f'(x) = sec²xcosx - tanxsinx
• f'(x) = sec²xcosx + tanxsinx
• f'(x) = sec²xsinx
• f'(x) = sec²xcosx - tanxcosx

Find the derivative of f(x) = -3x⁴cscx

• f'(x) = 12x³cscxcotx

• f'(x) = -3x⁴cscxcotx

• f'(x) =-12x³cscx + 3x⁴cotxcscx

• f'(x) = -3xcosx

y = (sinx)/x

find y’

• y' = (cosx)/x

• y' = (xcosx - sinx)/x²

• y' = (cosx - sinx)/x

• y' = (sinx - xcosx)/x²

Tags

CCSS.HSA.APR.D.6

Which of the following is the derivative of the function h(x)= (8x⁶ + 2x + 5)^{4 ?}

• h^'(x)= 4(8x⁶ + 2x + 5)³(48x⁵ + 2)

• h^'(x)= 4(48x⁵ + 2)³

• h^'(x)= 4(48x⁵ + 2 + 5)³

• h^'(x)= 3(8x⁶ + 2x + 5)⁴(48x⁵ + 2)²

Find  $\frac{dp}{dq}\ if\ p=\frac{1}{\sqrt{q+9}}$  

HINT: rewrite the square root as an exponent in the numerator

•  $-\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}$  

•  $\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}$  

•  $-\frac{1}{\left(q+9\right)^{\frac{3}{2}}}$  

•  $-\frac{1}{\sqrt{q+9}}$  

Find the derivative:  $\sin^2\left(3x+2\right)$  

•  $6\sin\left(3x+2\right)\cos\left(3x+2\right)$  

•  $-6\sin\left(3x+2\right)\cos\left(3x+2\right)$  

•  $6\cos\left(3x+2\right)$  

•  $-6\cos\left(3x+2\right)$  

Find dy/dx

• A

• B

• C

• D

Find the derivative.
f(x) = -8x^-3 + 5x - e^x

• f'(x) = -24x^-4 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x
• f'(x) = 24x^-2 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x-1

Tags

CCSS.HSF.IF.A.2

Find the second derivative of
f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx
• f"(x) = 2x + e^x + cosx
• f"(x) = 2x + xe^x - cosx
• f"(x) = 2x + e^x + sinx

Tags

CCSS.HSF.IF.A.2