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

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

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

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

x + 2 y

Solution steps

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

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

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

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

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

= 0 + 2 y + x

Simplify

= x + 2 y

\frac{d}{d x} (\frac{10}{( 1 - x ) ^{3}})

\int (- \frac{6}{x ^{4}}) d x

\int \frac{2 x - 3}{( x ^{2} + 2 x - 3 ) ^{\frac{3}{2}}} d x

2^{t}

\int \frac{8 x - 2}{x ^{2} - 1} d x

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