What is (\partial)/(\partial y)(6xy^2-6x^2y+5xy) ?

The answer to (\partial)/(\partial y)(6xy^2-6x^2y+5xy) is 12xy-6x^2+5x

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(\partial)/(\partial y)(6xy^2-6x^2y+5xy)

\frac{\partial}{\partial y} (6 x y^{2} - 6 x^{2} y + 5 x y)

12 x y - 6 x^{2} + 5 x

Solution steps

\frac{\partial}{\partial y} (6 x y^{2} - 6 x^{2} y + 5 x y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (6 x y^{2}) - \frac{\partial}{\partial y} (6 x^{2} y) + \frac{\partial}{\partial y} (5 x y)

\frac{\partial}{\partial y} (6 x y^{2}) = 12 x y

\frac{\partial}{\partial y} (6 x^{2} y) = 6 x^{2}

\frac{\partial}{\partial y} (5 x y) = 5 x

= 12 x y - 6 x^{2} + 5 x

x^{4} - 5 x^{2} + 4

\frac{d}{d x} (e^{s i n (2 x)} + sin (e^{2 x}))

x \to 2 lim (\frac{1}{x ( x - 2 )})

\frac{\partial}{\partial x} (x^{2} y + x y^{3})

x \to \infty lim (\frac{2}{3})

What is (\partial)/(\partial y)(6xy^2-6x^2y+5xy) ?
The answer to (\partial)/(\partial y)(6xy^2-6x^2y+5xy) is 12xy-6x^2+5x