Hello friends, Welcome to our blog Gamma Maths. Here you will get all the derivative formulas which will help you in your Class 11 and 12 studies. If you are preparing for your exams, you should definitely memorise these formulas, because they are very important for calculus.
What are derivative formulas
In simple words, derivative formulas are used to find the derivative of a specific function with respect to its independent variable. There are different types of derivative formulas for different functions. In this post, I have provided all the important formulas.
Basic Derivatives Formulas
Logarithmic Formulas
Trigonometric Formulas
Inverse Trigonometric Formulas
Hyperbolic Formulas
Inverse Hyperbolic Formulas
Differentiation Rules
Basic Derivatives Formulas
- \(\frac{d}{dx}(c)=0\)
- \(\frac{d}{dx}(x)=1\)
- \(\frac{d}{dx}(x^n)=n x^{n-1}\)
- \(\frac{d}{dx}(e^x)=e^x\)
- \(\frac{d}{dx}(a^x)=a^x\ln a\)
- \(\frac{d}{dx}(x^0)=0\)
- \(\frac{d}{dx}(\sqrt{x})=\frac{1}{2\sqrt{x}}\)
- \(\frac{d}{dx}\left(\frac{1}{x}\right)=-\frac{1}{x^2}\)
Logarithmic Functions
- \(\frac{d}{dx}(\ln x)=\frac{1}{x}\)
- \(\frac{d}{dx}(\ln|x|)=\frac{1}{x}\)
- \(\frac{d}{dx}(\log_a x)=\frac{1}{x\ln a}\)
- \(\frac{d}{dx}(\log x)=\frac{1}{x\ln 10}\)
Trigonometric Functions
- \(\frac{d}{dx}(\sin x)=\cos x\)
- \(\frac{d}{dx}(\cos x)=-\sin x\)
- \(\frac{d}{dx}(\tan x)=\sec^2 x\)
- \(\frac{d}{dx}(\cot x)=-\csc^2 x\)
- \(\frac{d}{dx}(\sec x)=\sec x\tan x\)
- \(\frac{d}{dx}(\cosec x)=-\csc x\cot x\)
Inverse Trigonometric Functions
- \(\frac{d}{dx}(\sin^{-1}x)=\frac{1}{\sqrt{1-x^2}}\)
- \(\frac{d}{dx}(\cos^{-1}x)=-\frac{1}{\sqrt{1-x^2}}\)
- \(\frac{d}{dx}(\tan^{-1}x)=\frac{1}{1+x^2}\)
- \(\frac{d}{dx}(\cot^{-1}x)=-\frac{1}{1+x^2}\)
- \(\frac{d}{dx}(\sec^{-1}x)=\frac{1}{|x|\sqrt{x^2-1}}\)
- \(\frac{d}{dx}(\cosec^{-1}x)= -\frac{1}{|x|\sqrt{x^2-1}}\)
Hyperbolic Functions
- \(\frac{d}{dx}(\sinh x)=\cosh x\)
- \(\frac{d}{dx}(\cosh x)=\sinh x\)
- \(\frac{d}{dx}(\tanh x)=\operatorname{sech}^2 x\)
- \(\frac{d}{dx}(\coth x)=-\operatorname{csch}^2 x\)
- \(\frac{d}{dx}(\operatorname{sech}x)= -\operatorname{sech}x\tanh x\)
- \(\frac{d}{dx}(\operatorname{csch}x)= -\operatorname{csch}x\coth x\)
Inverse Hyperbolic Functions
- \(\frac{d}{dx}(\sinh^{-1}x)=\frac{1}{\sqrt{x^2+1}}\)
- \(\frac{d}{dx}(\cosh^{-1}x)=\frac{1}{\sqrt{x^2-1}}\)
- \(\frac{d}{dx}(\tanh^{-1}x)=\frac{1}{1-x^2}\)
- \(\frac{d}{dx}(\coth^{-1}x)=\frac{1}{1-x^2}\)
- \(\frac{d}{dx}(\operatorname{sech}^{-1}x)= -\frac{1}{x\sqrt{1-x^2}}\)
- \(\frac{d}{dx}(\operatorname{cosech}^{-1}x)= -\frac{1}{|x|\sqrt{1+x^2}}\)
Rules of Differentiation
Here are some important differentiation rules that you should memorize.
- \(\frac{d}{dx}[u \pm v]=u' \pm v'\)
- \(\frac{d}{dx}[cu]=c\frac{du}{dx}\)
- \(\frac{d}{dx}[uv]=u\frac{dv}{dx}+v\frac{du}{dx}\)
- \(\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}\)
- \(\frac{d}{dx}[u^v]=u^v\left(v'\ln u+\frac{vu'}{u}\right)\)
- \(\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)\)
I will keep posting more helpful information and study tools, so please make sure to share this article with your friends and teachers. Thank you