# What is the derivative of #sin 5x#?

##### 1 Answer

Jan 19, 2016

#### Explanation:

Use the chain rule.

The chain rule states that, in the case of a sine function,

#d/dx[sinu]=cosu*(du)/dx#

More generally, the chain rule says to identify an inside function and an outside function. Here, the outside function is

The chain rule then says to differentiate the outside function, and the derivative of

The final step of this is to multiply the function by the derivative of the inside function, and the derivative of

Thus, the derivative of the whole function is

Using the rule given at the top:

#d/dx[sin5x]=cos5x*d/dx[5x]=cos5x*5=5cos5x#