Jaweria
  • Jaweria
Find dy/dx: 4x^2+3xy^2-6x^2y=y^3.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
abb0t
  • abb0t
Using implicit differentiation with respect to x. This means that you take the derivative of everything, even y, but everytime you take the deriviative of y, you multiply it by y'. For instance:\[\frac{ dy }{ dx }(x+y) = 1+\frac{ dy }{ dx } = 1+y'\] then, using your algebra skills, rearrange to find dy/dx
Jaweria
  • Jaweria
ahan ok
abb0t
  • abb0t
Remember: \[3xy^2 = 3x \frac{ d }{ dx}y^2+y^2\frac{ d }{ dx }3x\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Jaweria
  • Jaweria
I m little bit confuse here
cwrw238
  • cwrw238
what you are doing is treating y as a function of x (which is implied in the expression)
abb0t
  • abb0t
Of course!
Jaweria
  • Jaweria
thanks :-)
abb0t
  • abb0t
Start by taking the derivative as you normally would for the left side of the function. And like @cwrw238 pointed out, you're treating y as a function of x.
Jaweria
  • Jaweria
ok
abb0t
  • abb0t
If it helps, you can break it down to see it more clearly: \[\frac{ d }{ dx }4x^2 =\] \[\frac{ d }{ dx }3xy^2 = (3x \times \frac{ d }{ dx }y^2)+(y^2\frac{ d }{ dx }3x) = [3x \times 2y \frac{ dy }{ dx }]+[y^2 \times 3]\] \[\frac{ d }{ dx }6x^2y = \] NOW, the right side: \[\frac{ d }{ dx }y^3 = 3y^2\frac{ dy }{ dx } \]

Looking for something else?

Not the answer you are looking for? Search for more explanations.