warmup for quiz on chain rule

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

What is the derivative of f(x) = sin x?

• f'(x) = csc x
• f'(x) = cos x
• f'(x) = tan x
• f'(x) = sin x

Find dy/dx for 
y = (x² + 1)³

• dy/dx = 3(x² + 1)²
• dy/dx = 3(2x)²
• dy/dx = 6x(x² + 1)²
• dy/dx = 2x(x² + 1)²

Tags

CCSS.HSF-BF.B.4A

 $\frac{d}{dx}\sin^2x=$  

• 2sin x

• 2(sin x)(cos x)

• 2cos x

• 2x(cos x)

 $\frac{d}{dx}\left(\sqrt{\tan x}\right)$  

•  $\frac{1}{2\sqrt{\sec^2x}}$  

•  $\frac{1}{2\sec x}\tan x$  

•  $\frac{1}{2\sqrt{\tan x}}\sec^2x$  

•  $\frac{1}{2\sec x}$  

 $y=\cos\left(x^2\right)$  
 $\frac{dy}{dx}=$  

•  $-\sin\left(2x\right)$  

•  $-\cos\left(x^2\right)\sin\left(2x\right)$  

•  $-x^2\sin\left(2x\right)$  

•  $-\sin\left(x^2\right)\cdot2x$  

•  $-\sin\left(2x^3\right)$