How do you find the derivative of #y = (sin x)^(ln x)#?
Use implicit differentiation along with the chain and product rules.
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: