You will need
  • a textbook of algebra for 9 grade.
The first thing you need to differentiate the functions is to know the basic table of derivatives. It can be found in any mathematical Handbook.
Basic table of derivatives.
In order to solve the problems associated with finding the derivative, you need to learn the basic rules. So, let's say we have two differentiable functions u and v and some constant value C.

Derivative of constants is always equal to zero: ()' = 0;

The constant is always imposed for the sign of the derivative: (cu)' = cu';

When finding the derivative of sum of two functions, you just need them to differentiate, and the results folded: (u+v)' = u'+v';

When finding the derivative of a product of two functions, you need the derivative of the first function times the second function and add the derivative of the second function multiplied by the first function: (u*v)' = u'*v+v'*u;

In order to find the derivative from a private two functions is necessary, from the product of the derivative of the dividend, multiplied by a function of the divisor, subtract the product of the derivative of the divisor, multiplied by a function of the dividend is divided by divisor function squared. (u/v)' = (u'*v-v'*u)/v^2;

If given a complex function, then multiply the derivative of the inner function and the derivative from the outside. Let y=u(v(x)), then y'(x)=y'(u)*v'(x).
Using the above-obtained knowledge, you can differentiate almost any function. So, let's look at some examples:

y=x^4, y'=4*x^(4-1)=4*x^3;

y=2*x^3*(e^x-x^2+6), y'=2*(3*x^2*(e^x-x^2+6)+x^3*(e^x-2*x));
Also there are challenges to calculating the derivative at a point. Imagine you are given the function y=e^(x^2+6x+5), you need to find the value of the function at x=1.
1) Find the derivative function: y'=e^(x^2-6x+5)*(2*x +6).

2) Calculate the value of the function at a given point y'(1)=8*e^0=8