How do you use implicit differentiation to find #(dy)/(dx)# given #1=3x+2x^2y^2#?

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Answer 1 · 2017-12-24T14:36:41

#dy/dx = (-3-4xy^2)/(4x^2y)#

Differentiate the equation through term by term. Remember you are differentiating with respect to #x# so when differentiating #x# we get:

#x -> 1#

but when differentiating with respect to #y# we get:

#y -> (dy)/(dx)#.

So:

#1=3x+2x^2y^2#

Differentiating gives:

#0=3+4xy^2 + 4x^2y (dy)/(dx)#

which we obtain using the chain and product rule on the #2x^2y^2# term. So we now re-arrange to get #(dy)/(dx)#:

#-> dy/dx = (-3-4xy^2)/(4x^2y)#