Calculus Derivatives #2

Find the derivative:

 $f\left(x\right)=12x^3-9x^2+11x-2$  

•  $f'\left(x\right)=36x^2-18x+11$  

•  $f'\left(x\right)=36x^2-81x+11$  

•  $f'\left(x\right)=12x^2-9x+11$  

•  $f'\left(x\right)=36x^2+18x-11$  

Find the derivative:

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

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

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

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

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

Find the derivative:

 $h\left(x\right)=\sqrt{x}-2x$   

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

•  $h'\left(x\right)=\frac{1}{2\sqrt{x}}+2$  

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

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

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

Find the derivative:
 $f\left(x\right)=x^2\sin x$  

•  $f'\left(x\right)=2x\sin x+x^2\cos x$  

•  $f'\left(x\right)=2x\sin x-x^2\cos x$  

•  $f'\left(x\right)=-2x\sin x+x^2\cos x$  

•  $f'\left(x\right)=2x\cos x$  

Tags

CCSS.HSF.IF.A.2

Find the derivative:
 $g\left(x\right)=\sec x\tan x$  

•  $g'\left(x\right)=\sec x\tan^2x+\sec^3x$  

•  $g'\left(x\right)=\sec x\tan^2x-\sec^3x$  

•  $g'\left(x\right)=-\sec x\tan^2x+\sec^3x$  

•  $g'\left(x\right)=\sec x\tan x\sec^2x=\sec^3x\tan x$  

 $h\left(x\right)=e^x\cos x$  

Find the derivative.

•  $h'\left(x\right)=e^x\cos x-e^x\sin x$  

•  $h'\left(x\right)=e^{x-1}\cos x-e^x\sin x$  

•  $h'\left(x\right)=e^x\cos x+e^x\sin x$  

•  $h'\left(x\right)=-e^x\sin x$  

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Find the derivative:
 $f\left(x\right)=\frac{x^2}{x-3}$  

•  $f'\left(x\right)=\frac{x^2-6x}{\left(x-3\right)^2}$  

•  $f'\left(x\right)=\frac{x^2+6x}{\left(x-3\right)^2}$  

•  $f'\left(x\right)=\frac{x^2-6x}{\left(x-3\right)^3}$  

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

Find the derivative:
 $f\left(x\right)=\frac{x+3}{x-1}$  

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

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

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

•  $f'\left(x\right)=\frac{1}{1}=1$  

Tags

CCSS.HSA.APR.D.7

Find the derivative:
 $f\left(x\right)=\frac{x}{\sin x}$  

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

•  $f'\left(x\right)=\frac{\sin x+x\cos x}{\sin^2x}$  

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

•  $f'\left(x\right)=\frac{1}{\cos x}=\sec x$  

Find the derivative:
 $f\left(x\right)=\left(x^2-3\right)^{10}$  

•  $f'\left(x\right)=20x\left(x^2-3\right)^9$  

•  $f'\left(x\right)=20\left(x^2-3\right)^9$  

•  $f'\left(x\right)=20x\left(x^2-3\right)^{11}$  

•  $f'\left(x\right)=20x\left(x^2+3\right)^9$