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Homework Statement
knowing that -9x^2 - 6y^3 = -10 => [tex]\frac{dy}{dx}[/tex] = [tex]\frac{M(x)}{18y^2}[/tex],
determine function M.
i would like to know how i can find M, I am not sure where to start
Last edited:
mlazos said:The solution is the following
[tex]-9x^{2}-6y^{3}=-10\Rightarrow[/tex]
[tex]-9x^{2}=6y^{3}-10\Rightarrow[/tex]
[tex]d(-9x^{2})=d(6y^{3}-10)\Rightarrow[/tex]
[tex]-18xdx=18y^{2}dy[/tex] since [tex]d(-10)=0[/tex] the derivative of a constant is 0
[tex]\frac{-18xdx}{dx}=18y^{2}\frac{dy}{dx}\Rightarrow[/tex]
[tex]-18x=18y^{2}\frac{dy}{dx}\Rightarrow[/tex]
[tex]\frac{dy}{dx}=\frac{-18x}{18y^{2}}\Rightarrow[/tex]
Since we know that
[tex]\frac{dy}{dx}=\frac{M(x)}{18y^{2}}\Rightarrow[/tex]
[tex]M(x)=-18x[/tex]
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.
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