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

1. 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

2. anonymous

ahan ok

3. abb0t

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

4. anonymous

I m little bit confuse here

5. cwrw238

what you are doing is treating y as a function of x (which is implied in the expression)

6. abb0t

Of course!

7. anonymous

thanks :-)

8. 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.

9. anonymous

ok

10. 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: $\frac{ d }{ dx }y^3 = 3y^2\frac{ dy }{ dx }$