Question

How do you differentiate `y=7^(x^2)`?

Answer 1

`y=7^(x^2) => y'=(2ln(7)x)7^(x^2)`

Explanation:

Since `forall r in RR, x^r=e^(rln(x))`

It is true that

`7^(x^2)=e^(x^2ln(7))`

Then by the chain rule `(f(g(x)))'=f'(g(x))g'(x)`

`=> (e^(x^2ln(7)))'=e^(x^2ln(7))2ln(7)x=7^(x^2)(2ln(7)x)`