Differentiation rules[Product, Quotient & 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.HSN.RN.A.2

CCSS.HSA.SSE.A.2

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

• 5e^5x+1

• e^5x

• 5e^5x

• 1

Tags

CCSS.HSF-IF.C.8B

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)

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

 $\frac{\text{d}}{\text{d}x}\left[\left(x^2-1\right)\left(x+7\right)\right]$  

•  $3x^2-14x-1$  

•  $3x^2+14x-1$  

•  $3x^2-14x+1$  

•  $3x^2+14x+1$  

Tags

CCSS.HSA.APR.A.1

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

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

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

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

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

Tags

CCSS.HSN.RN.A.2