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

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= 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)

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Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.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

 $\frac{dy}{dx}\ if\ y=^3\sqrt{x^2\ }+x^e$  Find

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

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

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

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

Tags

CCSS.HSN.RN.A.2

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

Find y' if y = tan(3x²+2).

• sec²(3x²+2)
• 6xsec²(3x²+2)
• 6xsec²x(3x²+2)
• sec²(6x)

Tags

CCSS.HSF.IF.A.2