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

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

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

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

- y^{2} - 2 x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 0 - 2 x - y^{2}

Simplify

= - y^{2} - 2 x

\int_{1}^{3} 3 x^{2} + \frac{1}{12 x ^{2}} d x

x \to 3 lim (- 4)

13 e^{4 t} \cdot e^{2}

\int_{\frac{1}{2}}^{5} 10 x ln (2 x) d x

f (x) = 5 x^{- 15}

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