What is (\partial)/(\partial y)(x^2-xy+9y^2) ?

The answer to (\partial)/(\partial y)(x^2-xy+9y^2) is 18y-x

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(\partial)/(\partial y)(x^2-xy+9y^2)

\frac{\partial}{\partial y} (x^{2} - x y + 9 y^{2})

18 y - x

Solution steps

\frac{\partial}{\partial y} (x^{2} - x y + 9 y^{2})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{2}) - \frac{\partial}{\partial y} (x y) + \frac{\partial}{\partial y} (9 y^{2})

\frac{\partial}{\partial y} (x^{2}) = 0

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

\frac{\partial}{\partial y} (9 y^{2}) = 18 y

= 0 - x + 18 y

Simplify

= 18 y - x

x sin (\frac{6}{x})

\frac{\partial}{\partial x} (9 e^{x y})

\frac{d}{d x} ((e^{l n (x)})^{2^{- x}})

\int \frac{12}{x ^{2} - 1} d x

\frac{d}{d x} (\frac{6 x}{e ^{x}})

What is (\partial)/(\partial y)(x^2-xy+9y^2) ?
The answer to (\partial)/(\partial y)(x^2-xy+9y^2) is 18y-x