More Chain Rule Practice

Find the derivative of  f(x) = (x⁶ + 4)⁵

• f '(x) = 5x⁵(x⁴ + 4)⁴
• f '(x) = 6x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁶(x⁶ + 4)⁴

Find the derivative of f(x)=(x³-2x)²

• 6x⁵ - 12x³+8x
• 6x⁵ - 16x³+8x
• x⁶-4x⁴+4x²
• 6x⁵ - 16x^3-8x

• A

• B

• C

• D

• A

• B

• C

• D

• E

find y' for y=(e^5x)+1

• 5e^5x+1

• e^5x

• 5e^5x

• 1

Tags

CCSS.HSF-IF.C.8B

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)

• 
• 
• 
• 

 $\frac{d}{dx}\ln\left(x^3+2x+1\right)=$  

•  $\frac{1}{3x^2+2}$  

•  $\frac{1}{x^3+2x+1}$  

•  $\frac{3x^2+2}{x^3+2x+1}$  

•  $\frac{5}{x+3}$  

 $\frac{d}{dx}f\left(g\left(x\right)\right)=$  

•  $f'\left(g'\left(x\right)\right)$  

•  $f'\left(g\left(x\right)\right)$  

•  $f'\left(g\left(x\right)\right)g'\left(x\right)$  

•  $f\left(g'\left(x\right)\right)$  

•  $f'\left(x\right)g\left(x\right)+g'\left(x\right)f\left(x\right)$  

 $y=\left(2x^2+1\right)^{\frac{4}{3}}$  
 $\frac{dy}{dx}=$  

•  $\frac{4}{3}\left(2x^2+1\right)^{\frac{1}{3}}$  

•  $\frac{16x}{3}\left(2x^2+1\right)^{\frac{1}{3}}$  

•  $\frac{4x}{3}\left(2x^2+1\right)^{\frac{1}{3}}$  

•  $\frac{16}{3}x^{\frac{1}{3}}$