What is (\partial)/(\partial x)(xy+z^3x-2yz) ?

The answer to (\partial)/(\partial x)(xy+z^3x-2yz) is y+z^3

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(\partial)/(\partial x)(xy+z^3x-2yz)

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

y + z^{3}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (z^{3} x) = z^{3}

\frac{\partial}{\partial x} (2 yz) = 0

= y + z^{3} - 0

Simplify

= y + z^{3}

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

\int_{- 1}^{2} (x + 2 - x^{2})^{2} d x

t \to 1 lim (f (t))

y^{^{''}} + 16 y = 5 sec (4 t)

\int \frac{1}{( s ^{2} - 2 s + 1 ) ^{2}} d s

What is (\partial)/(\partial x)(xy+z^3x-2yz) ?
The answer to (\partial)/(\partial x)(xy+z^3x-2yz) is y+z^3