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

The answer to (\partial)/(\partial x)(e^{xyz}+xyz) is e^{xyz}yz+yz

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

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

e^{x yz} yz + yz

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= e^{x yz} yz + yz

\frac{d}{d x} ((3 x + 4) x^{2})

\int \frac{1}{n ^{2} + 1}

\int x cos (x y) d y

\frac{d}{d x} (ln (4 x^{2} + 1))

\frac{d}{d x} (1000 (1 - e^{- 0.15 x}))

What is (\partial)/(\partial x)(e^{xyz}+xyz) ?
The answer to (\partial)/(\partial x)(e^{xyz}+xyz) is e^{xyz}yz+yz