What is (\partial)/(\partial y)(3x-4xy+9y) ?

The answer to (\partial)/(\partial y)(3x-4xy+9y) is -4x+9

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(\partial)/(\partial y)(3x-4xy+9y)

\frac{\partial}{\partial y} (3 x - 4 x y + 9 y)

- 4 x + 9

Solution steps

\frac{\partial}{\partial y} (3 x - 4 x y + 9 y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (3 x) - \frac{\partial}{\partial y} (4 x y) + \frac{\partial}{\partial y} (9 y)

\frac{\partial}{\partial y} (3 x) = 0

\frac{\partial}{\partial y} (4 x y) = 4 x

\frac{\partial}{\partial y} (9 y) = 9

= 0 - 4 x + 9

Simplify

= - 4 x + 9

\frac{d}{d x} (\frac{x - 2}{x - 1})

\int_{0}^{1} 5 x - 5 x^{2} d x

\frac{( s + 1 ) ^{2}}{s ^{2} - s - 6}

\frac{\partial}{\partial x} (sin (6 x^{3} y - 6 x y^{2}))

\frac{d}{d x} (\frac{7}{x ^{8} + 5 x + 1})

What is (\partial)/(\partial y)(3x-4xy+9y) ?
The answer to (\partial)/(\partial y)(3x-4xy+9y) is -4x+9