Find the partial derivatives of the function f(x,y) = xye^(-6y)

partial-derivatives

#1

Find the partial derivatives of the function f(x,y) = xye^(-6y)

Answer:

f(x,y)=xye^(-6y)
df/dx keeping y as constant
df/dx=ye^(-6y)dx/dx=ye^(-6y)
df/dy , keeping x terms as constant.
df/dy=x {d(ye^(-6y))/dy} = x[ y {d(e^(-6y)/dy}+e^(-6y) d(y)/dy)]
df/dy= x{-6ye^(-6y)+e^(-6y)}
df/dy=-6xy e^(-6y)+e^(-6y)