Derivative Rules

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:

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

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

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

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

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

The General Power Rule says that

 $\frac{d}{dx}\left[x^n\right]=$  

•  $nx^{n-1}$  

•  $x^{n-1}$  

•  $nx^n$  

•  $x^n$  

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 of:

 $f\left(x\right)=\frac{3}{4}x-8$  

•  $\frac{3}{4}$  

• 3

• 4

•  $-8$  

Tags

CCSS.HSF.IF.A.2

Find the derivative:

 $f\left(t\right)=\frac{1}{t}-\frac{3}{t^2}+\frac{5}{t^3}$  

•  $f'\left(t\right)=-\frac{1}{t^2}+\frac{6}{t^3}-\frac{15}{t^4}$  

•  $f'\left(t\right)=-t^{-2}+6t^{-3}-15t^{-4}$  

•  $f'\left(t\right)=t^{-1}-3t^{-2}+5t^{-3}$  

•  $f'\left(t\right)=\frac{1}{t^2}+\frac{6}{t^3}-\frac{15}{t^4}$  

Tags

CCSS.HSA.APR.D.7

Find the derivative:

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

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

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

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

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

How do you rewrite this in power form:

 $f\left(t\right)=\frac{1}{t}-\frac{3}{t^2}+\frac{5}{t^3}$  

•  $f\left(t\right)=t^{-1}-3t^{-2}+5t^{-3}$  

•  $f\left(t\right)=-t^{-2}+6t^{-3}-15t^{-4}$  

•  $f\left(t\right)=-t^{-2}+t^{-3}-t^{-4}$  

•  $f\left(t\right)=\ t^{-2}-6t^{-3}+15t^{-4}$   

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

How can you change this to power form:

 $f\left(x\right)=4\sqrt{x}$  

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

•  $f\left(x\right)=2\sqrt{x}$  

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

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

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

CCSS.HSN.RN.A.2

Find the derivative of:

 $f\left(x\right)=3x^7-6x^6-10x^4+3x^3-15x-21$  

•  $f'\left(x\right)=21x^6-36x^5-40x^3+9x^2-15$  

•  $f'\left(x\right)=3x^6-6x^5-10x^3+3x^2-15$  

•  $f'\left(x\right)=x^6-x^5-x^3+x^2-15$  

•  $f'\left(x\right)=28x^6-30x^5-30x^3+12x^2-15$