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

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

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

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

y + 2 y x + y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= y + 2 y x + y^{2}

\frac{\partial}{\partial x} (e^{- 2 x^{2}})

\frac{\partial}{\partial s} (4 s^{3} t^{2} + 2 s t)

8 y^{^{''}} - 32 y = 0

cos (\frac{π}{4})

\frac{\partial}{\partial x} (ln (t^{2} + x^{2}))

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