Calculus Chain Rule

Multiple Choice

What is $$\frac{d}{dx}\left(\cos\left(x^3\right)\right)\ \ \ \ \ ?$$

• $$6x\ \cos\left(3x^3\right)$$

• $$-3x^2\ \sin\left(x^3\right)$$

• $$3x^2\ \sin\left(x^3\right)$$

• $$x^3\ \sin\left(x^3\right)$$

• $$3x^2\ \cos\left(x^3\right)$$

Multiple Choice

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

Multiple Choice

find y' for y= (2x+1)¹⁰

• 10(2x+1)⁹

• 20(2x-1)⁹

• 20(2x+1)¹⁰

• 20(2x+1)⁹

Multiple Choice

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)

Multiple Choice

Differentiate:
f(x) = x⁷ (5 + 8x)³

• f '(x) = x² (5 + 8x)⁶ (35 + 80x)
• f '(x) = x⁶ (5 + 8x)² (35 + 80x)
• f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)
• f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

Multiple Choice

Multiple Choice

Find y' if

y=tan(6x-19)

• y'= sec² (6x-19)

• y'= 6tan (6x-19)

• y'= 6sec² (6x-19)

• y'= 6csc² (6x-19)

Fill in the Blanks

Fill in the blank: What is the chain rule for the derivative?

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

Multiple Choice

Find the derivative of: $$6x\sqrt[]{x+5}$$  

• $$\frac{6}{\sqrt[]{x+5}}$$  

• $$\frac{9x+30}{\sqrt[]{x+5}}$$  

• $$\frac{-3}{\sqrt[]{x+5}}$$  

• $$6x+\frac{1}{2\sqrt[]{x+5}}$$