How do you differentiate #g(x) = e^xsqrt(1-e^(2x))# using the product rule?
Hey there! To differentiate a function using the product rule, keep note of the general formula for the derivative of a product whereby if:
Lets get started!
In this example, lets just change
Now, if you follow the derivative general formula, it reads "derivative of the 1st, times the 2nd - plus derivative of the 2nd times the 1st. Lets get those derivatives separately:
Now, sub everything in:
And that's it! One suggestion I do have; if you can do these "inner" derivative in your head and as you go(i.e. the chain rule we had to do), this will allow you to complete the question much faster. I only did the derivatives separately for demonstrative purposes.
Hopefully this helped and was clear for you! If you have any questions, please let me know! :)