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
3. Addition and Difference ‘Rule.
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
_ 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)
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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