How do you differentiate # f(x)=cos(e^((lnx-2)^2 ))# using the chain rule.?
The chain rule says that
or that if you have one function inside another, the derivative of the whole thing will be the derivative of the inside multiplied by the derivative of the outside (with the inside left the same).
Here, I've used
Based on the property that
Now, based on the chain rule again,
Now we have the derivative of the inside of the original function. The derivative of the outside bit with the inside left the same is just