How do you differentiate #f(x)=lnx^2*e^(x^3-1)# using the product rule?
We can start by using the chain rule to take the derivative of our first term,
Thus, we get
By the product rule, since we've taken the derivative of the first term, we multiply by the second term, which we leave alone.
This gives us, so far:
Now we do the same thing to the other term. We take the derivative of
By the product rule, we then add these two resulting terms together.
This can be further simplified as: