## Determine M(x)

1. The problem statement, all variables and given/known data
knowing that -9x^2 - 6y^3 = -10 => $$\frac{dy}{dx}$$ = $$\frac{M(x)}{18y^2}$$,

determine function M.

i would like to know how i can find M, im not sure where to start

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 Recognitions: Homework Help Science Advisor Differentiate the equation on the left with respect to x. Then solve for dy/dx.
 the equation on the left gives me -18x, what does the left one help me with getting M?

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## Determine M(x)

d/dx(y)=dy/dx, not zero. Use the chain rule to find d/dx(6*y^3).

 i don´t understand very well...is there a way i can put it in mathematica 6 to just get the solution?
 Recognitions: Homework Help Science Advisor This isn't difficult. You should be thinking of y as y(x), a function of x. E.g. d/dx(y(x)^2)=2*y(x)*dy(x)/dx. The dy/dx comes from the chain rule. If you want to try to find this in a textbook, look up 'implicit differentiation'.
 i got dy/dx = -x/y^2...now how can i apply to get M? sry for dumb questions :S
 The solution is the following $$-9x^{2}-6y^{3}=-10\Rightarrow$$ $$-9x^{2}=6y^{3}-10\Rightarrow$$ $$d(-9x^{2})=d(6y^{3}-10)\Rightarrow$$ $$-18xdx=18y^{2}dy$$ since $$d(-10)=0$$ the derivative of a constant is 0 $$\frac{-18xdx}{dx}=18y^{2}\frac{dy}{dx}\Rightarrow$$ $$-18x=18y^{2}\frac{dy}{dx}\Rightarrow$$ $$\frac{dy}{dx}=\frac{-18x}{18y^{2}}\Rightarrow$$ Since we know that $$\frac{dy}{dx}=\frac{M(x)}{18y^{2}}\Rightarrow$$ $$M(x)=-18x$$ You should have known the solution though, was pretty easy, my suggestion is to read more about implicit differentiation since many times can solve problems where other ways fail.
 Recognitions: Homework Help Science Advisor Good! Multiply by 1=18/18. So your answer could also be written -18x/(18*y^2).

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 Quote by mlazos The solution is the following $$-9x^{2}-6y^{3}=-10\Rightarrow$$ $$-9x^{2}=6y^{3}-10\Rightarrow$$ $$d(-9x^{2})=d(6y^{3}-10)\Rightarrow$$ $$-18xdx=18y^{2}dy$$ since $$d(-10)=0$$ the derivative of a constant is 0 $$\frac{-18xdx}{dx}=18y^{2}\frac{dy}{dx}\Rightarrow$$ $$-18x=18y^{2}\frac{dy}{dx}\Rightarrow$$ $$\frac{dy}{dx}=\frac{-18x}{18y^{2}}\Rightarrow$$ Since we know that $$\frac{dy}{dx}=\frac{M(x)}{18y^{2}}\Rightarrow$$ $$M(x)=-18x$$ You should have known the solution though, was pretty easy, my suggestion is to read more about implicit differentiation since many times can solve problems where other ways fail.
 $$-7\,y{e^{10\,{\it xy}}}=5$$ ==> $${\frac {{\it dx}}{{\it dy}}}={\frac {M \left( y \right) }{1+10\,{\it xy}}}$$ i did $${\frac {d \left( -7\,{{\it ye}}^{10\,{\it xy}} \right) }{{\it dy}}}={ \frac {d \left( 5 \right) }{{\it dy}}}$$ is it wrong way ?