SOLUTION: If {{{xy+3x+y^2=21}}} defines a differentiable implicit function y=f(x), find {{{dy/dx}}} in terms of x and y.

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Question 995895: If xy%2B3x%2By%5E2=21 defines a differentiable implicit function y=f(x), find dy%2Fdx in terms of x and y.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
If xy%2B3x%2By%5E2=21 defines a differentiable implicit function y=f(x), find dy%2Fdx in terms of x and y.
xy%2B3x%2By%5E2=21

Differentiate each term, using differentiation formulas
you have studied:



Simplifying

x%2Aexpr%28%28dy%29%2F%28dx%29%29%2By%2B3%2B2y%2Aexpr%28%28dy%29%2F%28dx%29%29=0

Isolate terms in %28dy%29%2F%28dx%29 on the left

x%2Aexpr%28%28dy%29%2F%28dx%29%29%2B2y%2Aexpr%28%28dy%29%2F%28dx%29%29=-y-3

Factor out %28dy%29%2F%28dx%29 on the left:

expr%28%28dy%29%2F%28dx%29%29%28x%2B2y%29=-y-3

Divide both sides by (x+2y)

expr%28%28dy%29%2F%28dx%29%29=%28-y-3%29%2F%28x%2B2y%29

Edwin