Chain Rule Practice

Find the derivative of $y=\left(x+6\right)^4\$  

•  $4\left(x+6\right)^3$  

•  $3\left(x+6\right)^4$  

•  $24\left(x+6\right)^3$  

•  $4\left(x+5\right)^3$  

Find the derivative of following with respect to x:

y = (2x + 1)¹⁰

• y' = 10(2x + 1)⁹

• y' = 20(2x - 1)⁹

• y' = 20(2x + 1)¹⁰

• y' = 20(2x + 1)⁹

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 for $y=\left(1-x^2\right)^5$  

•  $\frac{dy}{dx}=-10x\left(1-x^2\right)^6$  

•  $\frac{dy}{dx}=10x\left(1-x^2\right)^4$  

•  $\frac{dy}{dx}=-10x\left(1-x^2\right)^4$  

•  $\frac{dy}{dx}=10\left(1-x^2\right)^4$  

Find the derivative.

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 $\frac{d}{dx}\sqrt{x^3-1}$  

•  $\sqrt{3x^2}$  

•  $\frac{1}{2\sqrt{x^3-1}}$  

•  $\frac{3x^2}{2\sqrt{x^3-1}}$  

• What ever Isaac Newton says

Find the derivative for $f\left(x\right)=\sqrt{1-2x^2}$  

•  $f'\left(x\right)=\frac{-2x}{\sqrt{1-2x^2}}$  

•  $f'\left(x\right)=\frac{2x}{\sqrt{1-2x^2}}$  

•  $f'\left(x\right)=-2x\sqrt{1-2x^2}$  

•  $f'\left(x\right)=\frac{-4x^2}{\sqrt{1-2x^2}}$  

Find the derivative.

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• 
• 
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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 an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x⁵ + 5)²

• y = 500x + 400
• y = 100x + 400
• y = -500 x - 400
• y = 500x - 400

Tags

CCSS.HSS.ID.C.7