Chain Rule & Higher Order Derivatives Review

Find the derivative of

 $f\left(x\right)=\left(x^3+1\right)^7$  

•  $7\left(3x^2+1\right)^6$  

•  $7\left(x^3+1\right)^6\left(3x^2\right)$  

•  $21x^2$  

•  $21x^2\left(x^{18}\right)$  

Find the derivative of

 $f\left(x\right)=\sqrt{x^2+8}$  

•  $\left(x^2+8\right)^{\frac{1}{2}}$  

•  $\frac{1}{2}\left(x^2+8\right)^{\frac{3}{2}}\left(2x\right)$  

•  $x\left(x^2+8\right)^{\frac{1}{2}}$  

•  $\frac{1}{2}\left(x^2+8\right)^{-\frac{1}{2}}\left(2x\right)$  

Tags

CCSS.HSN.RN.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Find the derivative of

 $f\left(x\right)=\frac{1}{x^4+3x}$  

•  $-\left(x^4+3x\right)^{-2}\left(4x^3+3\right)$  

•  $\left(x^4+3x\right)^{-2}\left(4x^3+3\right)$  

•  $\left(x^4+3x\right)^2\left(4x^3-3\right)$  

•  $-\left(x^4+3x\right)^2\left(4x^3\right)$  

Tags

CCSS.HSA.APR.D.7

Find the derivative of

 $f\left(x\right)=4x\left(3x-1\right)^2$  

•  $24x\left(3x-1\right)^{-1}+\left(3x-1\right)^2$  

•  $24x\left(3x-1\right)+4\left(3x-1\right)^2$  

•  $24x\left(3x-1\right)^2+\left(3x-1\right)^2$  

•  $8x\left(3x-1\right)+12x$  

Find the derivative of

 $y=\left(e^{2x}+e^x\right)^{\frac{1}{2}}$ 

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

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

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

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

Tags

CCSS.HSN.RN.A.2

CCSS.HSN.RN.A.1

Find the derivative of

 $y=\ln\left(5x^2+9\right)^3$ 

•  $\frac{1}{\left(5x^2+9\right)^3}3\left(5x^2+9\right)^2\left(10x\right)$  

•  $\frac{1}{\left(5x^2+9\right)^3}3\left(5x^2+9\right)^2$  

•  $\frac{1}{\ln\left(5x^2+9\right)^3}3\left(5x^2+9\right)^2\left(10x\right)$  

•  $\frac{10x}{\left(5x^2+9\right)^3}$  

Tags

CCSS.HSF.BF.B.5

Find the derivative of

 $y=\frac{x}{\sin\ 3x}$ 

•  $\frac{\sin3x+\cos3x}{\left(\sin3x\right)^2}$  

•  $\frac{\sin3x-3\cos3x}{\left(\sin3x\right)^2}$  

•  $\frac{\sin3x+3x\cos3x}{\left(\sin3x\right)^2}$  

•  $\frac{\sin3x-3x\cos3x}{\left(\sin3x\right)^2}$  

Find the derivative of

 $y=e^{\tan x}$ 

•  $e^{\tan x}$  

•  $e^{\tan x}\left(\sec^2x\right)$  

•  $e^{\tan x}\left(-\sec^2x\right)$  

•  $e^{\tan x}\left(\cot\ x\right)$  

Tags

CCSS.HSN.RN.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Find the THIRD derivative of

 $y=\cos8x$ 

• -8 sin 8x

• -64 sin 8x

• 512 sin 8x

• -64 cos 8x