Find $\dfrac{dy}{dx}$, where $x^3-3xy^3+x^2+y^2+7=0$ How am I supposed to extract $y$ as a function of $x$ fom that equation? Thank you!
Derivative of $y$. Where $y$ is the solution of one ecuation.
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$\begingroup$
calculus
derivatives
partial-derivative
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3Is this from a chapter on implicit differentiation by any chance? – 2017-01-05
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0I don't know exactly where it is from. It is from an exam...so can't tell! – 2017-01-05
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2Okay let me rephrase: you have to use implicit differentiation. – 2017-01-05
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0These downvoters really annoy me: it is obvious that the OP doesn't know that the problem is solved with implicit differentiation, so he is painfully and mistakenly looking to express $y$ as a function of $x$. Mathematicians are supposed to be intelligent and to be able to read between the lines, but I don't see this in all this downvoting. – 2017-01-05
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0@DenisNichita: So far you have asked 16 questions but only accepted 2 answers. On behalf of the Math.SE users, I apologize for us not being up to your level of excellence. – 2017-01-07
1 Answers
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assuming that we have $$y=y(x)$$ then we get by differentiating with respect to $x$ $$3x^2-3y^3-3x\cdot 3y^2\cdot y'+2x+2y\cdot y'=0$$
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0Where did you get $-3x3y^2y'$ and $2yy'$? – 2017-01-05
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0@DenisNichita As I had said before two times, implicit differentiation – 2017-01-05