chain Rules

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

• 5e^5x+1

• e^5x

• 5e^5x

• 1

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)

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)

 $\frac{\text{d}}{\text{d}x}\left[\left(2x+1\right)\left(5x-4\right)\right]$  

•  $10x-3$  

•  $20x-4$  

•  $10x-4$  

•  $20x-3$  

Tags

CCSS.HSA.APR.A.1

 $\frac{\text{d}}{\text{d}x}\left[\left(\sqrt{x}\right)\left(x-1\right)\right]$  

•  $\frac{3}{2}x^{\frac{1}{2}}+\frac{1}{2}x^{\frac{-1}{2}}$  

•  $\frac{3}{2}x^{\frac{1}{2}}-\frac{1}{2}x^{\frac{-1}{2}}$  

•  $\frac{1}{2}x^{\frac{1}{2}}-\frac{3}{2}x^{\frac{-1}{2}}$  

•  $\frac{1}{2}x^{\frac{1}{2}}+\frac{3}{2}x^{\frac{-1}{2}}$  

 $\frac{\text{d}}{\text{d}x}\left[x^2\cdot\sin\left(x\right)\right]$  

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

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

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

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

What rule should be used in deriving h(x) = 2(x - 4)³

• Power rule

• Product rule

• Quotient rule

• Chain rule

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴
• f'(t) = 5(t² + 2t)⁴
•  f'(t) = 5(t² + 2t)⁴(2t)
• f'(t) = 5(t² + 2t)⁴(2t + 2)

Which option shows the derivative?

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