y=ln(x^2)(e^x)

Question

calculate y'

Answer 1

First, this equation can be simplified to:

 

y = 2ln(x)e^x

 

Using the product rule, we know that

 

If y = f(x)g(x), then y' = f'(x)g(x) + f(x)g'(x)

 

Let f(x) = ln(x)

Let g(x) = e^x

 

We know that f'(x) = 1/x

We know that g'(x) = e^x

 

Therefore:

 

y' = 2(1/x * e^x + ln(x)*e^x)

= 2e^x/x + 2e^xln(x)