## Jaweria Group Title Find dy/dx: 4x^2+3xy^2-6x^2y=y^3. one year ago one year ago

1. abb0t Group Title

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. Jaweria Group Title

ahan ok

3. abb0t Group Title

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

4. Jaweria Group Title

I m little bit confuse here

5. cwrw238 Group Title

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

6. abb0t Group Title

Of course!

7. Jaweria Group Title

thanks :-)

8. abb0t Group Title

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. Jaweria Group Title

ok

10. abb0t Group Title

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