Finding of a derivative (differentiation) - one of the main tasks of the mathematical analysis. Finding of derivative function has a set of applications in physics and mathematics. Consider an algorithm.
Instruction
1. Simplify function. Present it in the form in which it is convenient to take a derivative.
2. Take a derivative, using rules of differentiation and the table of derivatives. In it there are derivatives of the main elementary functions: linear, sedate, indicative, logarithmic, trigonometrical, return trigonometrical. It is desirable to know derivatives of elementary functions by heart.
3. The derivative of constant (unchangeable) function is equal to zero. Example of unchangeable function: y=5.
4. Rules of differentiation. Let with - constant number, u(x) and v(x) - some differentiable function.1) (cu) of '=cu'; 2) (u+v) of '=u '+v'; 3) (u-v) of '=u '-v'; 4) (uv) '=u'v+v'u; 5) (u/v) '= (u'v-v'u)/v^2В a case of difficult function needs to take consistently derivatives of the elementary functions which are a part of difficult function and to multiply them. Consider that in difficult function one function is an argument of other function. Let's review an example. (cos(5x-2)) of '=cos'(5x-2) * (5x-2) '=-sin(5x-2) *5=-5sin(5x-2). In this example we consistently take a derivative of function of a cosine with an argument (5x-2) and a derivative of linear function (5x-2) with an argument x. We multiply derivatives.
5. Simplify the received expression.
6. If it is necessary to find a function derivative in the set point, substitute value of this point in the received expression for a derivative.