How do you differentiate # f(x)= (7e^x+x)^2 # using the chain rule.?
With the chain rule, if you have some composition of functions that looks like
then the derivative
Essentially, differentiate the outside function while treating the whole inside function as if it's a single variable, and multiply it by the derivative of the inside function.
To illustrate what I mean, just imagine
Then we have
So, to find the derivative, we'll just apply the formula we have above.
The derivative of
And, the derivative of
Let's plug all that in:
And there's our answer.