Question

`sin(3x+5)` find differentiate ?

Answer 1

`3cos(3x+5)`

Explanation:

What we have here is a composite function, and whenever we're taking the derivative of a composite function, it helps to use the Chain Rule.

`sin(3x+5)` is composed of the functions `sinx` and `3x+5`. I'll define the following:

• `f(x)=sinx`
• `g(x)=3x+5`

Given this, the Chain Rule tells us that the derivative of `sin(3x+5)` will be:

`f'(g(x))*g'(x)`

Let's differentiate `f` and `g`. We get:

• `f'(x)=cosx`
• `g'(x)=3`

Let's plug in! We get:

`cos(3x+5)*3`

Which can be rewritten as:

`3cos(3x+5)`