To find the derivative of composite functions

To solve complex integration problems

To simplify algebraic expressions

To calculate the limit of a function

To simplify complex functions into simpler components

To understand the power of derivatives

To differentiate composite functions

To master the chain rule

To find the derivative of composite functions

To simplify complex functions

To solve equations involving derivatives

To evaluate limits of functions

$$x^2+2x+3$$  

$$4x^2+3$$  

$$2x^2+3$$  

$$2x^2+6$$  

10(2x+1)⁹

20(2x-1)⁹

20(2x+1)¹⁰

20(2x+1)⁹

Comparison

Integration

Derivatives

Multiplication

warning

Chain rule

Product rule

Quotient rule

Sum rule

when there is a function in a function (composition of functions)

when there is division of two functions

when there is product of two functions

Product rule

Quotient rule

Power rule

Sum rule

Chain rule

Quotient rule

Power rule

Product rule

anytime you want

when there is a function in a function (composition of functions)

when there is division of two functions

when there is product of two functions

$$f'\left(x\right)=9x^2-18x+11$$  

$$f'\left(x\right)=9x^3-18x^2+11$$  

$$f'\left(x\right)=3x^2-9x+11$$  

$$f'\left(x\right)=9x-18$$  

$$f'\left(x\right)=2x\cos x$$  

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

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

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

$$g'\left(x\right)=2x^2+15x-27$$  

$$g'\left(x\right)=4x+15$$  

$$g'\left(x\right)=2$$  

$$g'\left(x\right)=2x$$  

$$h'\left(x\right)=x^2-9+4x^{-1}$$  

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

$$h'\left(x\right)=2x+\frac{4}{x^2}$$  

$$h'\left(x\right)=2x-\frac{4}{x}$$  

$$\frac{dy}{dx}=\frac{2}{3x^{\frac{1}{3}}}+\frac{1}{x^{\frac{3}{4}}}$$  

$$\frac{dy}{dx}=-\frac{2}{3x^{\frac{1}{3}}}+\frac{1}{x^{\frac{3}{4}}}$$  

$$\frac{dy}{dx}=\frac{2}{3x^{\frac{1}{3}}}-\frac{1}{x^{\frac{3}{4}}}$$  

$$\frac{dy}{dx}=-\frac{2}{3x^{\frac{1}{3}}}-\frac{1}{x^{\frac{3}{4}}}$$  

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

$$f'\left(x\right)=-\frac{1}{x^2}+\frac{2}{x^3}-\frac{3}{x^4}$$  

$$f'\left(x\right)=\frac{1}{x^2}+\frac{2}{x^3}-\frac{3}{x^4}$$  

$$f'\left(x\right)=-\frac{1}{x^2}-\frac{2}{x^3}-\frac{3}{x^4}$$  

f '(x) = 5x⁵(x⁴ + 4)⁴

f '(x) = 6x⁵(x⁶ + 4)⁴

f '(x) = 30x⁵(x⁶ + 4)⁴

f '(x) = 30x⁶(x⁶ + 4)⁴

f'(t) = 5(2t + 2)⁴

$$3\left(\frac{x}{2x+1}\right)^2$$  

$$3\left[\frac{1}{\left(2x+1\right)^2}\right]^2$$  

$$\frac{1}{2}$$  

$$\frac{3x^2}{\left(2x+1\right)^4}$$  

$$f'\left(x\right)=\sqrt{x^2-1}$$  

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

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

$$f'\left(x\right)=x\sqrt{x^2-1}$$  

$$f'\left(x\right)=2x-3$$  

$$f'\left(x\right)=\frac{1}{2x-3}$$  

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

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

$$f'\left(x\right)=\frac{1}{2x}$$  

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

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

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

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

$$f'\left(x\right)=2^{x^2-3}\ ·\ \ln2\ ·\ 2x$$  

$$f'\left(x\right)=2^{x^2-3}$$  

$$f'\left(x\right)=2^{x^2-3}\ ·\ \ln2$$