Product & Quotient Rule

Rewrite then find the derivative using the power rule. $f\left(x\right)=\frac{3x^3+2x^2+4x}{x}$  

•  $f'\left(x\right)=6x+2$  

•  $f'\left(x\right)=9x+4+4x^{-1}$  

•  $9x^2+4x+4$  

•  $\frac{6x^3+4x^2+8x}{x^2}$  

Tags

CCSS.HSF-IF.C.8B

Rewrite and find the derivative using the power rule.  $f\left(x\right)=\frac{3}{x}$  

•  $f'\left(x\right)=3$  

•  $f'\left(x\right)=3x^{-1}$  

•  $f'\left(x\right)=-3x^{-2}$  

•  $f'\left(x\right)=3x^{-3}$  

find the derivative of f(x).  $f\left(x\right)=\left(x+2\right)\left(x-5\right)$  

•  $f'\left(x\right)=2x^2-3x-10$  

•  $f'\left(x\right)=x^2-3x-10$  

•  $f'\left(x\right)=2x-3$  

•  $f'\left(x\right)=2x-13$  

FInd the derivative of f(x). $f\left(x\right)=\left(2x-3\right)^2$  

•  $f'\left(x\right)=4x-12$  

•  $f'\left(x\right)=8x-12$  

•  $f'\left(x\right)=4x^2-12x+9$  

•  $f'\left(x\right)=4x-6$  

Use the quotient rule to find the derivative of f(x).  $f\left(x\right)=\frac{2x+3}{3x-5}$  

•  $f'\left(x\right)=\frac{2}{3}$  

•  $f'\left(x\right)=-\frac{1}{\left(3x-5\right)^2}$  

•  $f'\left(x\right)=-\frac{19}{9}$  

•  $f'\left(x\right)=-\frac{19}{\left(3x-5\right)^2}$  

Use the quotient rule to find the derivative of f(x). $f\left(x\right)=\frac{x^2+5}{x^2-9}$  

•  $f'\left(x\right)=-\frac{8x}{\left(x^2-9\right)^2}$  

•  $f'\left(x\right)=-\frac{29x}{\left(x^2-9\right)^2}$  

•  $f'\left(x\right)=\frac{2x+5}{2x-9}$  

•  $f'\left(x\right)=1$  

Which is the unsimplified derivative of f(x) using the product rule.  $f\left(x\right)=\left(2x+3\right)\left(x-5\right)$  

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

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

•  $f'\left(x\right)=2$  

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

 $f\left(x\right)=\sqrt{x}\left(x^3-5x\right)$  Which is the unsimplified derivative of f(x) using the product rule.

•  $f'\left(x\right)=\frac{1}{2}x^{-\frac{1}{2}}\left(3x^2-5\right)$  

•  $f'\left(x\right)=\sqrt{x}\left(3x^2-5\right)$  

•  $f'\left(x\right)=x^{\frac{1}{2}}\left(3x^2-5\right)$  

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