Question

what is the first partial dervative of f(x,y)=x^y to the respect of y

Answer 1

treat x like a contstant
what is the derivative of f(y)=3^y
lnf(y)=ln3^y
lnf(y)=yln3
f'(y)/f(y)=ln3
f'(y)=ln3*f(y)
f'(y)=ln3*3^y
so if we have f(x,y)=x^y, then f_y=lnx*x^y

Answer 2

brb i have to brush my teeth

Answer 3

lnf(y)=yln3,f'(y)/f(y)=ln3 how this step is pertformed?

Answer 4

i took derivative of both sides

Answer 5

what is the derivative of f(x)=ln(x^2-1)

Answer 6

f'(x)=(x^2-1)'/(x^2-1)=2x/(x^2-1)

Answer 7

that sounds about right. i am going to try it out

Answer 8

yay fun

Answer 9

thank you

Answer 10

great! i'm glad it worked out for you

Answer 11

who gave me that medal?
thanks whoever
lol