Final Exam- Calculus

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

.

• (3x²-2)cos(x³-2x)

• -(3x²-2)cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)

Find the slope-intercept form equation for tangent line to :
 $y=\frac{x+1}{x-1}\ ,\ where\ x\ne1$  

Find all points on this graph where the tangent line is horizontal:
 $y=\frac{1}{x^2}-\frac{1}{x^3}$  

Find dy/dx if y = sec(8x²).

• sec(16x)tan(16x)
• 16xcos(8x²)
• 16xsecxtanx(8x²)
• 16xsec(8x²)tan(8x²)

Find the derivative of  $y=\ln\sqrt{x}$  

•  $y'=\frac{1}{\sqrt{x}}$  

•  $y'=\frac{1}{x}$  

•  $y'=\frac{1}{2x}$  

•  $y'=\sqrt{x}$  

Find the derivative of  $y=\frac{\ln x}{x}$  

•  $y'=\frac{1}{x^2}$  

•  $y'=\frac{1}{x}$  

•  $y=\frac{1-\ln x}{x^2}$  

•  $y'=\frac{x-\ln x}{x^2}$  

 $y=2x^{3\ }+\ 3x^2-36x+40$  

A particle moving on the x-axis has the above position after an elapsed time of x seconds.

What is the total distance traveled by the particle during the first 3 seconds?

• 12x⁴ +3x²
• 20x⁴ +3x² +16
• 3x⁵ +32x³ +6x² +8x
• 24x³

Tags

CCSS.HSA.APR.A.1

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴
• f'(t) = 5(t² + 2t)⁴
•  f'(t) = 5(t² + 2t)⁴(2t)
• f'(t) = 5(t² + 2t)⁴(2t + 2)