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

The answer to (\partial)/(\partial x)(x+y^2+x^2y) is 2xy+1

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

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

2 x y + 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

= 1 + 0 + 2 y x

Simplify

= 2 x y + 1

\int 2^{t} d t

\frac{1}{x ^{2} - x + 1}

\frac{\partial}{\partial x} (x y^{2} z^{3} + 3 yz)

\frac{\partial}{\partial y} (x^{3} + y^{2} - 5 x y)

\frac{\partial}{\partial y} (4 - x^{2} - y^{2})

What is (\partial)/(\partial x)(x+y^2+x^2y) ?
The answer to (\partial)/(\partial x)(x+y^2+x^2y) is 2xy+1