# How do you find the derivative of #y = (sin x)^(ln x)#?

##### 1 Answer

Use implicit differentiation along with the chain and product rules.

#### Explanation:

We can find the derivative of this function implicitly. In other words, we will find the derivative of

First, we want to get rid of the

Now, we derive both sides. For the left side, we will have the derivative of

So, the left side of the equation now looks like this:

Now we take the derivative of the right side, which we can do using the product and chain rules. We get:

Remember that we're trying to solve for

Finally, to get our answer back into terms of

Our final answer is: