Guys, huge problem: what is the derivative from this
3x^2*y^2-5x+siny=(3y-1)^4
I really need to solve this, but i don't even know where to start.
Guest
First of all, that makes no sense. You find the derivative of a function, not an equation. I will assume that you are to find the derivative of y with respect to x, dy/dx.
Using the chain rule, the derivative of [tex]y^2[/tex] with respect to x is the derivative of [tex]y^2[/tex] with respect to y times the derivative of y with respect to x: [tex]2y\frac{dy}{dx}[/tex] so the derivative of [tex]3x^2y^2[/tex] with respect to x is, by the product rule, [tex]6xy^2+ 6x^2y\frac{dy}{dx}[/tex]. Similarly the derivative of [tex]sin(y)[/tex] with respect to x is [tex]cos(y)\frac{dy}{dx}[/tex] and the derivative of [tex](3y- 1)^4[/tex] with respect to x is [tex]4(3y- 1)^3(3)\frac{dy}{dx}= 12(3y- 1)^3\frac{dy}{dx}[/tex]
So, differentiating both sides of [tex]3x^2*y^2-5x+siny=(3y-1)^4[/tex] with respect to x we get [tex]6xy^2+ 6x^2y\frac{dy}{dx}- 5+ cos(y)\frac{dy}{dx}= 12(3y- 1)^3\frac{dy}{dx}[/tex]. Finally, solve that for [tex]\frac{dy}{dx}[/tex].