Chain Rule

What is your first name?

What is your Last Name?

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

find y' for y= (2x+1)¹⁰

• 10(2x+1)⁹

• 20(2x-1)⁹

• 20(2x+1)¹⁰

• 20(2x+1)⁹

Tags

CCSS.HSA.APR.C.5

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)

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

Find  $\frac{dy}{dx}\ if\ y=\frac{x^3}{x-1}$  

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

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

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

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

Tags

CCSS.HSA.APR.D.6

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

•  $\left(12x+4\right)\left(2x^2+4\right)^2$  

•  $3\left(2x^2+4\right)^2$  

•  $12x\left(2x^2+4\right)^2$  

•  $12\left(2x^2+4\right)^2$  

Tags

CCSS.HSA.APR.A.1

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

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

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

•  $-\sin\sqrt{10t+12}$  

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