Question

Find derivative of sin(x+1) ?

Answer 1

`cos(x+1)`

Explanation:

Let ,`f(x)=color(red)(sin)(x+1)`

`f^'(x)=color(red)(cos)(x+1)d/(dx)color(blue)((x+1)`

`f'(x)=cos(x+1)*color(blue)(1`

`:. f'(x)=cos(x+1)`

To apply the chain rule to this problem, the derivative of the outside function is multiplied by the derivative of the inside function. The outside function is the `sin` function, and the inside function is the `(x+1)`.

The derivative of `color(red)(sintheta` is `color(red)(costheta` and the derivative of `color(blue)((x+1)` is just `color(blue)(1`. This is shown in the second step. Remember that when the chain rule is applied to the outside function, the inside function remains the same, hence why it is `cos(x+1)` instead of `cosx`.

Hope this helps.