f(x,y)=x^2 e^2x lny (2,1)

Question

I need to find the partial derivatives with respect to x and y. I have not idea how to do this especially with the (2,1).

Answer 1

f(x,y)=(x^2)(e^2x)lny
f’x=((x^2)(e^2x))’lny= ((x^2)’(e^2x)+x^2(e^2x)’)lny=(2xe^2x+2x^2e^2x)lny=2xe^2x(1+x)lny
f’y=(x^2e^2x)(lny)’=x^2e^2x/y