Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm confused about some points in implicit equation ...

From my recitation class -

$G(x,y)=0$ provides - $y=f(x)$ .

And $f'(x)=\frac{dy}{dx}$

and about $G'(x,y)=0$ we use -

enter image description here

How would be look $f'(x)$ in case of the follow implicit equation ? -

enter image description here

share|cite|improve this question
up vote 1 down vote accepted

I have usually seen this called an implicit function. You are not guaranteed the ability to transform it into the form $y=f(x)$, but you can do implicit differentiation. From $3x^7+2y^5-x^3+y^3-3=0$ you take a derivative with respect to $x$ to get $21x^6+10y^4y'-3x^2+3y^2y'=0, y'=-\frac{21x^6-3x^2}{10y^4+3y^2}$

share|cite|improve this answer

You have

$$G(x,y)=3x^7+2y^5-x^3+y^3-3=0 $$


$$\frac{\partial G}{\partial x}=21x^6-3x^2 $$

$$\frac{\partial G}{\partial y}=10y^4+3y^2 $$


$$\frac{dy}{dx}=-\frac{\frac{\partial G}{\partial x}}{\frac{\partial G}{\partial y}}=-\frac{21x^6-3x^2}{10y^4+3y^2} $$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.