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

The answer to (\partial)/(\partial y)(x^2-xy+5y^2) is 10y-x

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

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

10 y - x

Solution steps

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

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

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

\frac{\partial}{\partial y} (5 y^{2}) = 10 y

= 0 - x + 10 y

Simplify

= 10 y - x

\int sin (7 π t) d t

\frac{d}{d x} (x^{3} arctan (5 x))

\int \frac{9 ( 1 - tan ^{2} ( x ) )}{sec ^{2} ( x )} d x

\frac{d}{d x} (csc (x) + cot (x))

\frac{ln ( x )}{5 x ^{3}}

What is (\partial)/(\partial y)(x^2-xy+5y^2) ?
The answer to (\partial)/(\partial y)(x^2-xy+5y^2) is 10y-x