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

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

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(\partial)/(\partial x)(yx^2+xy^2+yz^2)

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

y^{2} + 2 y x

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

= 2 y x + y^{2} + 0

Simplify

= y^{2} + 2 y x

\int \frac{e ^{x} ( 1 + x )}{cos ^{2} ( x e ^{x} )} d x

\frac{d}{d x} (\frac{x}{8} - \frac{8}{x})

f (x) = sin (x), (0, 0)

(1.7) (10.8)

\int_{1}^{10} \frac{33}{x ^{3}} d x

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