Differentiation : formulas, basics and easy method to learn

Basics

In calculus, differentiation is one of the two important concepts apart from integration. Differentiation is a method of finding the derivative. Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables. The most common example is the rate change of displacement with respect to time, called velocity. The opposite of finding a derivative is anti-differentiation.

Differentiation formula

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If x is a variable and y is another variable, then the rate of change of x with respect to y is given by dy/dx. This is the general expression of derivative of a function and is represented as f'(x) = dy/dx, where y = f(x) is any function. 

Differentiation Formulas

The important formulas are given below in the table. Here, let us consider f(x) as a function and f'(x) is the derivative of the function.

If f(x) = tan (x), then f'(x) = sec2x If f(x) = cos (x), then f'(x) = -sin x If f(x) = sin (x), then f'(x) = cos x If f(x) = ln(x), then f'(x) = 1/x If f(x) = ex, then f'(x) = ex If f(x) = xn, where n is any fraction or integer, then f'(x) = nxn-1 If f(x) = k, where k is a constant, then f'(x) = 0