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.

You can download it by clicking on highlighted Download PDF.

Topics on this page:

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

Download PDF

Some basic differentiation Formula

These are basic rule fore defferention.

\(\frac{d}{dx}x^n=nx^{n-1}\)
\(\frac{d}{dx}x=1\)
\(\frac{d}{dx}√x=\frac{1}{2√x}\)
\(\frac{d}{dx}a=0\)

Differentiation Formula ,whare u and v are function of x

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

\(\frac{d}{dx}au=a\frac{d}{dx}u\)
\(\frac{d}{dx}(u+v)=\frac{d}{dx}u+\frac{d}{dx}v\)
\(\frac{d}{dx}(u-v)=\frac{d}{dx}u-\frac{d}{dx}v\)
\(\frac{d}{dx}(uv)=u\frac{d}{dx}v+v\frac{d}{dx}u\)
\(\frac{d}{dx}(\frac{u}{v})=\frac{v\frac{d}{dx}u-u\frac{d}{dx}v}{v^2}\)

Differentiation Formula for trigonometric function

\(\frac{d}{dx}sinx=cosx\)
\(\frac{d}{dx}cosx=-sinx\)
\(\frac{d}{dx}tanx=sec^2x\)
\(\frac{d}{dx}cotx=-cosec^2x\)
\(\frac{d}{dx}secx=secx tanx \)
\(\frac{d}{dx} cosecx=-cosecx cotx \)

Differentiation Formula for inverse trigonometric function

\(\frac{d}{dx}sin^{-1}x=\frac{1}{\sqrt{1-x^2}}\)
\(\frac{d}{dx}cos^{-1}x=-\frac{1}{\sqrt{1-x^2}}\)
\(\frac{d}{dx}tan^{-1}x=\frac{1}{1+x^2}\)
\(\frac{d}{dx}cot^{-1}x=-\frac{1}{1+x^2}\)
\(\frac{d}{dx}sec^{-1}x=\frac{1}{|x|\sqrt{x^2-1}}\)
\(\frac{d}{dx}cosec^{-1}x=-\frac{1}{|x|\sqrt{x^2-1}}\)

Differentiation Formula for power and logarithmic function

\(\frac{d}{dx}a^x=a^x lna\)
\(\frac{d}{dx}e^x=e^x\)
\(\frac{d}{dx}e^{mx}=me^mx\)
\(\frac{d}{dx}lnx=\frac{1}{x};(x>0)\)
\(\frac{d}{dx}log_ax=\frac{1}{x lna}=\frac{1}{x}log_a e\)