Derivatives Test

Find the derivative of  $f\left(x\right)=\sec^24x$  

•  $2\sec^24x\tan4x$  

•  $8\sec^2x\tan x$  

•  $8x\sec4x\tan4x$  

•  $8\sec^24x\tan4x$  

Find the derivative of  $f\left(x\right)=3\sin\left(2x-1\right)$  

•  $6\cos\left(2x-1_{ }\right)$  

•  $-6\cos\left(2x-1\right)$  

•  $3\cos\left(2x-1\right)$  

•  $-3\cos\left(2x-1\right)$  

Find the derivative of  $y=5\ln\left(6x-2\right)$  

•  $\frac{5}{6x-2}$  

•  $\frac{30}{6x-2}$  

•  $\frac{6}{30x-10}$  

•  $\frac{6}{6x-2}$  

Find the derivative of  $y=\ln\left(\frac{4}{x-1}\right)$  

•  $\frac{1}{x-1}$  

•  $\ln4-\frac{1}{x-1}$  

•  $-\frac{1}{x-1}$  

•  $\ln4+\frac{1}{x-1}$  

Find the derivative of  $y=7e^{2x}$  

•  $14e^{2x}$  

•  $14xe^{2x}$  

•  $7e^{2x}$  

•  $\frac{7}{2}e^{2x}$  

What is the derivative of

  $y=e^2\ln x$  

•  $\frac{1}{x}$  

•  $\frac{e^2}{x}$  

•  $\frac{1}{e^2x}$  

•  $2$  

Find the equation of the tangent line to the graph of  $f\left(x\right)=2x^2-2x+3$  at the point where x = 1.

•  $y=2x-2$  

•  $y=2x+1$  

•  $y=4x^{ }-2$  

•  $y=4x+1$  

All of the following are rules to take derivatives EXCEPT

• chain rule

• product rule

• quotient rule

• tangent rule

Set up the derivative of y=(3x⁴ - 7)(5x² + 1)

• (12x³)(10x)

• (3x⁴ - 7)(10x) + (12x³)(5x² + 1)

• (3x⁴ - 7)(10x) - (12x³)(5x² + 1)

• (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Find dy/dx by Implicit Differentiation 
x³ +y³  = 36

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0