Question

If f(y) = e^(9y) + e^(-9y), find f'(y). Use exact values.

Answer 1

Given:

`f(y)=e^(9y)+e^(-9y)`

To find:

The f'(y).

Solution:

Chain rule of differentiation:

`[f(g(x))]'=f'(g(x))g'(x)`

Differentiation of exponential:

`(d)/(dx)e^x=e^x`

We have,

`f(y)=e^(9y)+e^(-9y)`

Differentiate with respect to y.

`f'(y)=e^(9y)(d)/(dx)(9y)+e^(-9y)(d)/(dx)(-9y)`

`f'(y)=e^(9y)\cdot 9(1)+e^(-9y)\cdot (-9)(1)`

`f'(y)=9e^(9y)-9e^(-9y)`

Therefore, the differentiation of the given function is
`f'(y)=9e^(9y)-9e^(-9y)`.