# Rules for Differentiation

Rules for Differentiation

The process of generating the derivative function is called differentiation. There are a series of rules which can be employed to differentiate the most common functions.These rules are called the rules of differentiation.

1.  Constant Rule

Given a function y = f(x) = ax where a is constant then             _ dx - 0. This is so because as y does not change its value,•thus Ay must be zero for all Ax including its limit.

2.  Power Rule.

Give a function y = f(x) = ax n where a is constant and x is a non-zero integer, then dx = naxn-1 i.e., multiply the original function by power and reduce the power by I

If y = f(x) can be written as the sum or difference of two functions i.e., y = u(x) + v(x) or y = u(x) – v(x)

a __dv dx dx dx

Then

_ du dv dx dx dx

4.  Chain Rule

If a function y = f(x) is a composite function y = g(u) where u = h(x).

then derivative of y with respect to xis equal to the product of the derivative of y with

_ dy du

respect to u and the derivative of u with respect to x i.e., dx – du • dx

5.  Exponential Rule

The derivative of the exponential function is the exponential function. If y = ex then 2 = ex..

6.  Product and Quotient Rule

Product Rule: If y = f(x) can be written .as the product of two functions i.e., y = u(x)

du

dx v(x) then the derivative of y with respect to x is       = u(x) .     +—dv

dx v(x)

This means that derivative of the product of two functions is equal to the first function multiplied by the derivative of the second function plus the second function multiplied by the derivative of the first fun

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