How do you find the derivative of #xy^2#?

1 Answer
Sep 14, 2015

If you want to differentiate this expression as part of an implicit differentiation problem, here is how:

Explanation:

Assuming that we want to find the derivative with respect to #x# of #xy^2# (assumong that #y# is a function of #x#:

First use the product rule:

#d/dx(xy^2) = d/dx(x) y^2 + x d/dx(y^2)#

Now for #d/dx(y^2)# we'll need the power and chain rules.

#d/dx(xy^2) = 1 y^2 + x [2y dy/dx]#

#d/dx(xy^2)= y^2 +2xy dy/dx#

If you want to differentiate the expression with respect to #t# then the derivatives above are all #d/dt# and #(dx)/dt# may not be #1#.

#d/dt(xy^2) = y^2dx/dt + 2xy dy/dt#

If you want the partial derivatives of the function #f(x,y) = xy^2# that has been answered in another answer.