# Find derivative of sin(x+1) ?

Apr 19, 2018

$\cos \left(x + 1\right)$

#### Explanation:

Let ,$f \left(x\right) = \textcolor{red}{\sin} \left(x + 1\right)$

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

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

$\therefore f ' \left(x\right) = \cos \left(x + 1\right)$

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 $\left(x + 1\right)$.

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 $\cos \left(x + 1\right)$ instead of $\cos x$.

Hope this helps.