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

Find the derivative of f(x)=(x³-2x)²

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

Tags

CCSS.HSA.APR.A.1

• A

• B

• C

• D

Tags

CCSS.HSA.SSE.A.2

CCSS.HSN.RN.A.2

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

• 5e^5x+1

• e^5x

• 5e^5x

• 1

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.LE.A.1

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)

• 
• 
• 
• 

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Find the derivative.
 f(z) = 1/(3z²) + 4z³

• f'(z) = 6z³ + 12z²
• f'(z) = 6z + 12x²
• f'(z) =  -2/(3z³) + 12z²
• f'(z) = -6/z² + 12z²

Find  $\frac{dv}{dt}\ if\ v=t+\frac{8}{t}$  

•  $1-\frac{8}{t^2}$  

•  $1-\frac{8}{t}$  

•  $t-\frac{8}{t^2}$  

•  $1+\frac{8}{t^2}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Find  $\frac{dp}{dq}\ if\ p=\frac{1}{\sqrt{q+9}}$  

•  $-\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}$  

•  $\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}$  

•  $-\frac{1}{\left(q+9\right)^{\frac{3}{2}}}$  

•  $-\frac{1}{\sqrt{q+9}}$  

Tags

CCSS.HSN.RN.A.2

 $\frac{dy}{dt}\ if\ y=\cos\sqrt{10t+12}$  Find

•  $\frac{-5}{\sqrt{10t+12}}\sin\sqrt{10t+12}$  

•  $\frac{-1}{2\sqrt{10t+12}}\sin\sqrt{10t+12}$  

•  $-\sin\sqrt{10t+12}$  

•  $-\sin\left(\frac{5}{\sqrt{10t+12}}\right)$