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

The answer to (\partial)/(\partial x)(x^2+zsin(xyz)) is 2x+z^2ycos(zyx)

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(\partial)/(\partial x)(x^2+zsin(xyz))

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

2 x + z^{2} y cos (zy x)

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (z sin (x yz)) = z^{2} y cos (zy x)

= 2 x + z^{2} y cos (zy x)

\int \frac{( 1 - u ^{2} - u - u ^{3} )}{1 + u ^{2}} d u

x^{2} - 3

\frac{d}{d z} (ln (\frac{b ^{2} - z ^{2}}{b ^{2} + z ^{2}}))

y^{^{''}} + 9 y = 4 csc^{2} (3 t)

x \to 0 lim (\frac{2 x}{tan ( x )})

What is (\partial)/(\partial x)(x^2+zsin(xyz)) ?
The answer to (\partial)/(\partial x)(x^2+zsin(xyz)) is 2x+z^2ycos(zyx)