I am unable to catch the derivatives of some common functions like f(X) = 1/x, x^2............
In some problems derivatives of functions are cubes of x + squares of x...........
please make me understand.
The golden rule of derivatives: for all $\displaystyle n\in\mathbb{R}\,,\,(x^n)'=nx^{n-1}$ (please note $\displaystyle n$ is REAL, not merely natural, integer or even rational: ANY real number)
For example, $\displaystyle (x^2)'=2x\,,\,(x^7)'=7x^6\,,\,\,\left(\frac{1}{x}\ right)'=\left(x^{-1}\right)'=(-1)x^{-2}=-x^{-2}=-\frac{1}{x^2}\,,$ $\displaystyle (\sqrt{x})'=(x^{1\slash 2})'=\frac{1}{2}x^{-1\slash 2}=\frac{1}{2\sqrt{x}}$ , ...etc.
Tonio
how about doing some research on your own first, then come back if you have a question about a specific derivative.
Pauls Online Notes : Calculus I