What is (\partial)/(\partial x)((z)(e^{xyz}+xy)) ?

The answer to (\partial)/(\partial x)((z)(e^{xyz}+xy)) is z(e^{xyz}zy+y)

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(\partial)/(\partial x)((z)(e^{xyz}+xy))

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

z (e^{x yz} zy + y)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (e^{x yz}) = e^{x yz} zy

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

= z (e^{x yz} zy + y)

\frac{2 ( - x ^{2} + 2 )}{( x ^{2} + 2 ) ^{2}}

\frac{1}{( 1 + k cos ( x ) ) ^{2}}

e^{2 t} (2 - t - 2 e^{- t})

((x - 2 L)^{2})^{2}

25 π (2 - \frac{x}{4})^{2}

What is (\partial)/(\partial x)((z)(e^{xyz}+xy)) ?
The answer to (\partial)/(\partial x)((z)(e^{xyz}+xy)) is z(e^{xyz}zy+y)