Question

Find dy/dx: 4x^2+3xy^2-6x^2y=y^3.

Answer 1

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

Answer 2

ahan ok

Answer 3

Remember: \[3xy^2 = 3x \frac{ d }{ dx}y^2+y^2\frac{ d }{ dx }3x\]

Answer 4

I m little bit confuse here

Answer 5

what you are doing is treating y as a function of x

(which is implied in the expression)

Answer 6

Of course!

Answer 7

thanks :-)

Answer 8

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.

Answer 9

ok

Answer 10

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: \[\frac{ d }{ dx }y^3 = 3y^2\frac{ dy }{ dx } \]