Question

Differentiate the function? y = (ln(1 + e^x))^5

Answer 1

`dy/dx=(5e^xln^4(1+e^x))/(1+e^x)`

Explanation:

`y=ln^5(1+e^x)`

By the chain rule,

`dy/dx=5ln^4(1+e^x)*d/dx[ln(1+e^x)]=5ln^4(1+e^x)*(d/dx(1+e^x))/(1+e^x)=(5e^xln^4(1+e^x))/(1+e^x)`