Derivatives of Logarithmic Functions

What is the derivative of ln(x)?

• xln(x)
• 1/x
• e^x
• ln(x+1)

Tags

CCSS.HSF-IF.C.8B

Find the derivative of  $y=\ln\left(8x\right)$  

•  $y'=\frac{1}{8x}$  

•  $y'=\frac{1}{x}$  

•  $y'=8x$  

•  $y'=x$  

Differentiate  $\ln\ \left(2x+3\right)$  

•  $\frac{1}{2x+3}$  

•  $\frac{2}{2x+3}$  

•  $2x+3$  

•  $-\left(2x+3\right)$  

• 1/(2x⁵)
• 1/(10x⁴)
• 2x⁵
• 5/x

Tags

CCSS.HSA.APR.D.7

Find the derivative of  $y=8\ln\left(x\right)+3x^2$  

•  $y'=\frac{8}{x}+6x$  

•  $y'=\frac{1}{x}+6x$  

•  $y'=14x$  

•  $y'=x$  

Find the derivative:
y = 3ln(x²-3)

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

• 1/(3x²+5)^1/4
• (3x)/(2(3x²+5))
• (2(3x²+5)^3/4)/(3x)
• (3x²+5)^1/4

• 1/(12x²)
• 3/x
• 1/(4x³)
• 4x³

Differentiate  $\ln\ \left(2-5x\right)^4$  

•  $\frac{1}{\left(2-5x\right)^4}$  

•  $\frac{20}{2-5x}$  

•  $\frac{20}{5x-2}$  

•  $-\frac{20}{\left(2-5x\right)^3}$  

Find the derivative:

y=ln(3x²-5x)

• (6x-5)/(3x²-5)

• 6x-5

• (x³/3)-(5x²)/2

• (6x-5)/(3x³-2x)