how to get the derivative of e^2x+x*e^x+x^2*lnx

Question

How to get the derivative of e^2x+x*e^x+x^2*lnx

Answer 1

if the given expression is called y, then y' is obtained by using the product rule and chain rule...

y' = 2e^2x + e^x +xe^x   + 2xlnx +x²(1/x)   which you can simplify (if desired)

Answer 2

f(x) = e^2x + xe^x + x²lnx

 

Use combinations of exponent, power, product, and chain rules, term by term.

 

f'(x) = 2e^2x + (e^x + xe^x) + (2xlnx + x²/x)

 

You can simplify it if you wish.