Question

Calculus: help me find the implicit differentiation of x^3-2x^2y+3xy^2=3

Help me use the Chain Rule at 3xy^2 .
I understand I will use the product rule on 2x^2y.

I prefer dy/dx, preference really.

Answer 1

Aha! my favorite area of math.

Answer 2

same, these were the days.... ahhh

Answer 3

with respect to which variable?

Answer 4

oh snap sorry I inserted the wrong snickers

Answer 5

\[ x^3-2x^2y+3xy^2=38
\] think of it as
\[x^3-2x^2f(x)+3xf^2(x)=38\] then take the derivative using the chain rule and the product rule

Answer 6

wait no I didn't so yeah \[x ^{3}-2y*x ^{2}+3x*y ^{2=38}\]
differentiating with respect to x , use product rule when required

Answer 7

\[3x ^{2} - 2[y.(2x) + x ^{2}.(dy/dx)] - 3[x.(2y)(dy/dx) + y ^{2}(dx/dx)] = 0 \]

Answer 8

\(dy/dx\) is a pain
easier to write
\[3x^2-2(2xy+x^2y')+3(y^2+2xyy')=0\]

Answer 9

sorry dy/dx makes it easier for me but you can change it if you'd like
\[dy/dx[-2x ^{2} - 6xy] = 4xy - 3x ^{2} + 3y ^{2} \]

Answer 10

and there you have it
\[dy/dx = (4xy - 3x ^{2} + 3y ^{2})/(-2x ^{2} - 6xy) = (3x ^{2} - 3y ^{2} - 4xy)/(2x ^{2} + 6xy) \]

Answer 11

@RJaza do you get it or nah?

Answer 12

@shelbygt520 still working on it! I like that you used dy/dx. Chain rule kills me.