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

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

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

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

y^{2} + y - 2 x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= y^{2} + y - 2 x

2 e^{x}

\int x + x ln (x) d x

\int t sin^{2} (t) d t

x \to - 6 lim (11 x)

5 e^{x} x

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