Derivative Rules

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Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

CCSS.HSA.REI.A.1

CCSS.HSA.SSE.A.1

Find the derivative of:

 $f\left(x\right)=\frac{2}{x^2}-\frac{9}{x}$  

•  $f'\left(x\right)=-\frac{4}{x^3}+\frac{9}{x^2}$  

•  $f'\left(x\right)=-\frac{4}{x}+9$  

•  $f'\left(x\right)=\frac{2}{x^3}-\frac{9}{x^2}$  

•  $f'\left(x\right)=\frac{4}{x^3}-\frac{9}{x^2}$  

Find the derivative of:

 $f\left(x\right)=x^9-7x^5+3x+13$  

•  $f'\left(x\right)=9x^8-35x^4+3$  

•  $f'\left(x\right)=x^8-7x^4+3$  

•  $f'\left(x\right)=9x^9-35x^5+3x$  

•  $f'\left(x\right)=9x^8-35x^4+3+13$  

Find the derivative of:

 $f\left(x\right)=4\sqrt{x}$  

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

•  $f'\left(x\right)=2\sqrt{x}$  

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

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

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

CCSS.HSN.RN.A.2

Find the derivative:

 $f\left(x\right)=x^{\frac{12}{5}}+3x^{\frac{7}{5}}$  

•  $f'\left(x\right)=\frac{12}{5}x^{\frac{7}{5}}+\frac{21}{5}x^{\frac{2}{5}}$  

•  $f'\left(x\right)=x^{\frac{7}{5}}+3x^{\frac{2}{5}}$  

•  $f'\left(x\right)=12x^{\frac{7}{5}}+21x^{\frac{2}{5}}$  

•  $f'\left(x\right)=\frac{12}{5}x^{\frac{4}{5}}+\frac{21}{5}x^{\frac{1}{5}}$  

Find the derivative:
y=4e^x²

• y'=8xe^x
• y'=8xe^x²
• y'=8xe^2x
• y'=8xe^4x²

Tags

CCSS.HSF-IF.C.8B

Find the derivative:

y=(2^3x+4)

• 3(ln2)(2^3x+4)

• 3(2^3x+4)

• 3(2^3x+4/(ln2))

• 2^3x+4

Tags

CCSS.HSF.BF.B.5

Find the derivative:

y=e^5x+ln(x)

• e^5+1/x

• e^5x+ln(x)

• (5+1/x) e^5x+ln(x)

• (5/x) e^5x+ln(x)

Tags

CCSS.HSF.BF.B.5

Find the derivative:
y = 3ln(x²-3)

• 6x/(x²-3)
• 3/(x²-3)
• 3x/(x²-3)
• 9x/(x²-3)

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Find the derivative:
y=5x²e^3x

• y'=10xe^3x(2x+3)
• y'=5xe^3x(3x+2)
• y'=10ex^3x(3x+2)
• y'=5xe^3x(2x+3)