What is (\partial)/(\partial x)(xze^{xz}) ?

The answer to (\partial)/(\partial x)(xze^{xz}) is z(e^{xz}+e^{xz}xz)

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(\partial)/(\partial x)(xze^{xz})

\frac{\partial}{\partial x} (x z e^{x z})

z (e^{x z} + e^{x z} x z)

Solution steps

\frac{\partial}{\partial x} (x z e^{x z})

Treat

z

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x z}

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

\frac{\partial}{\partial x} (x) = 1

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

= z (1 \cdot e^{x z} + e^{x z} z x)

Simplify

= z (e^{x z} + e^{x z} x z)

cos (sin (tan (9 x)))

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f (x) = \frac{sin ( x )}{x ^{2}}

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What is (\partial)/(\partial x)(xze^{xz}) ?
The answer to (\partial)/(\partial x)(xze^{xz}) is z(e^{xz}+e^{xz}xz)