What is (\partial)/(\partial x)(yx^2z^2-xy^4+xz) ?

The answer to (\partial)/(\partial x)(yx^2z^2-xy^4+xz) is 2yz^2x-y^4+z

(\partial)/(\partial x)(yx^2z^2-xy^4+xz)

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

2 y z^{2} x - y^{4} + z

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (x y^{4}) = y^{4}

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

= 2 y z^{2} x - y^{4} + z

\frac{d}{d x} (ln (x) cos (x))

x^{2} y^{^{''}} + 3 x y^{^{'}} - 15 y = 0

in v erse l a pl a ce \frac{6}{s ^{2} + 5 s + 6}

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

t an g e n t \frac{1}{x}, at x = 3

What is (\partial)/(\partial x)(yx^2z^2-xy^4+xz) ?
The answer to (\partial)/(\partial x)(yx^2z^2-xy^4+xz) is 2yz^2x-y^4+z