12 - Linearity Rule for differentiation - I

Let y=kf(x)  , where k  is a constant. Then

dy dx = lim h0 kf(x+h)kf(x) h

=k lim h0 f(x+h)f(x) h

=k f (x)

Here are few examples where this rule is applied to find the derivatives in such cases.

1. Let y=3 x 4  , then dy dx =3 d dx ( x 4 )=(3)(4 x 3 )=12 x 3

2. Let y=2 x 3  , then dy dx =2 d dx ( x 3 )=(2)(3 x 4 )=6 x 4

3. y=4 x =4 x 1 2  , then dy dx =4 d dx ( x 1 2 )=(4)( 1 2 x 1 2 )=2 x 1 2