What is (\partial)/(\partial x)(x^3+y^3+xy) ?

The answer to (\partial)/(\partial x)(x^3+y^3+xy) is 3x^2+y

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(\partial)/(\partial x)(x^3+y^3+xy)

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

3 x^{2} + y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

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

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

= 3 x^{2} + 0 + y

Simplify

= 3 x^{2} + y

\int \frac{7 sin ( 2 x )}{1 + cos ^{4} ( x )} d x

\frac{d}{d x} ((x^{11} - 2)^{3})

x^{2} (x^{3} + 5)^{3}

\int \frac{w + 1}{w ^{2} + 2 w} d w

What is (\partial)/(\partial x)(x^3+y^3+xy) ?
The answer to (\partial)/(\partial x)(x^3+y^3+xy) is 3x^2+y