Derivatives of Exponential and Log Functions

If  $y=e^{-2x^3}$  , then  $\frac{\text{d}y}{\text{d}x}=$  

•  $-2x^3e^{-2x^3}$  

•  $e^{-2x^3}$  

•  $-6x^2e^{-2x^3}$  

•  $e^{-6x^2}$  

•  $-6x^2e^{-6x^2}$  

Differentiating  $\frac{\left(e^{2x}-e^x\right)^2}{e^x}$  yields:

•  $3e^{3x}+e^x$  

•  $3e^{3x}-4e^{2x}+e^x$  

•  $e^{3x}-e^{2x}+e^x$  

•  $e^{3x}+e^x$  

•  $\frac{1}{3}e^{3x}-e^{2x}+e^x$  

Differentiating  $-\log_e\left(2x-3\right)$  yields:

•  $\frac{2}{2x-3}$  

•  $\frac{-1}{2x-3}$  

•  $\frac{1}{2x-3}$  

•  $\frac{2}{3-2x}$  

•  $\frac{-3}{2x-3}$  

If $y=x^2e^{3x}$  then  $\frac{\text{d}y}{\text{d}x}=$  

•  $6xe^{3x}$  

•  $2xe^{3x}$  

•  $\left(3x^2+2x\right)e^{3x}$  

•  $\left(x^2+1\right)e^{3x}$  

•  $\left(x^2+x\right)e^{3x}$  

If  $f\left(x\right)=\frac{e^{\left(x+1\right)}}{x+1},$   then the exact value of $f'\left(-1\right)$  is:

•  $\frac{3e^2}{4}$  

•  $0$  

•  $\frac{e^2}{4}$  

•  $-\frac{e^2}{4}$  

•  $\frac{-3e^2}{4}$  

Differentiating  $-\log_e\sqrt{16-x^2}$  yields:

•  $\frac{x}{\sqrt{16-x^2}}$  

•  $\frac{-x}{\sqrt{16-x^2}}$  

•  $\frac{2x}{x^2-16}$  

•  $\frac{2x}{16-x^2}$  

•  $\frac{-2x}{\sqrt{16-x^2}}$  

Find the derivative:

y=log₄(6x+5))

• (ln4)(1/(6x+5))

• (6ln4)/(6x+5)

• 6/((ln4)(6x+5))

• 6/(6x+5)

Find the derivative:
y = 3ln(x²-3)

• 6x/(x²-3)
• 3/(x²-3)
• 3x/(x²-3)
• 9x/(x²-3)

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Find the derivative:

y=log₉x

• y′=1 /((log9)x)

• y′=(ln9)/x

• y′=1/(x(lnx))

• y′=1/((ln9)x)

Tags

CCSS.HSF-IF.C.8B

The derivative of y = ln(cosx) is...

• y' = -tanx

• y' = -secx

• y'= secx

• y' = tanx