The rule for differentiation for a standard function y = xn also works when the function has rational indices, i.e. n is a rational number (either a fraction or decimal number)
= n
Let us look at a few examples of fractional indices:
Example 1: y = 4
Write y = 4 , and then apply
= 4
= 4 x
= 1 x
=
=
Example 2: y =
Write y = =
=
=
= =
=
Example 3: y =
= =
=
=
= =
Example 4: Find the equation of tangent to the curve y = at the point (1, 2)
y = =
= 2 x
=
At x = 1, m = =
=
Equation of tangent at (1, 2) is
y – 2 = (x – 1)
3y – 6 = -4x + 4
4x + 3y – 10 = 0