# Differentiation Formula

Differentiation is an important topic for higher class mathematics and science related subjects.  Here I have shared most of the common used formula for differentiation. Students can refer these to solve their mathematical problems. I have suplied a PDF version of this page.

• basic differentiation formula,
•  differentiation formula for trigonometric function,
• differentiation formula for inverse trigonometric functions and
• differentiation formula for power and logarithmic function.

## Some basic differentiation Formula

These are basic rule fore defferention.
1. $$\frac{d}{dx}x^n=nx^{n-1}$$
2. $$\frac{d}{dx}x=1$$
3. $$\frac{d}{dx}√x=\frac{1}{2√x}$$
4. $$\frac{d}{dx}a=0$$

### Differentiation Formula ,whare u and v are function of x

Here we have considered u and v as function of x .

1. $$\frac{d}{dx}au=a\frac{d}{dx}u$$
2. $$\frac{d}{dx}(u+v)=\frac{d}{dx}u+\frac{d}{dx}v$$
3. $$\frac{d}{dx}(u-v)=\frac{d}{dx}u-\frac{d}{dx}v$$
4. $$\frac{d}{dx}(uv)=u\frac{d}{dx}v+v\frac{d}{dx}u$$
5. $$\frac{d}{dx}(\frac{u}{v})=\frac{v\frac{d}{dx}u-u\frac{d}{dx}v}{v^2}$$

## Differentiation Formula for trigonometric function

1. $$\frac{d}{dx}sinx=cosx$$
2. $$\frac{d}{dx}cosx=-sinx$$
3. $$\frac{d}{dx}tanx=sec^2x$$
4. $$\frac{d}{dx}cotx=-cosec^2x$$
5. $$\frac{d}{dx}secx=secx tanx$$
6. $$\frac{d}{dx} cosecx=-cosecx cotx$$

## Differentiation Formula for inverse trigonometric function

1.  $$\frac{d}{dx}sin^{-1}x=\frac{1}{\sqrt{1-x^2}}$$
2. $$\frac{d}{dx}cos^{-1}x=-\frac{1}{\sqrt{1-x^2}}$$
3. $$\frac{d}{dx}tan^{-1}x=\frac{1}{1+x^2}$$
4. $$\frac{d}{dx}cot^{-1}x=-\frac{1}{1+x^2}$$
5. $$\frac{d}{dx}sec^{-1}x=\frac{1}{|x|\sqrt{x^2-1}}$$
6. $$\frac{d}{dx}cosec^{-1}x=-\frac{1}{|x|\sqrt{x^2-1}}$$

## Differentiation Formula for power and logarithmic function

1. $$\frac{d}{dx}a^x=a^x lna$$
2. $$\frac{d}{dx}e^x=e^x$$
3. $$\frac{d}{dx}e^{mx}=me^mx$$
4. $$\frac{d}{dx}lnx=\frac{1}{x};(x>0)$$
5. $$\frac{d}{dx}log_ax=\frac{1}{x lna}=\frac{1}{x}log_a e$$