What is (\partial)/(\partial z)(3ze^{xyz}) ?

The answer to (\partial)/(\partial z)(3ze^{xyz}) is 3(e^{zxy}+e^{zxy}zxy)

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(\partial)/(\partial z)(3ze^{xyz})

\frac{\partial}{\partial z} (3 z e^{x yz})

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

Solution steps

\frac{\partial}{\partial z} (3 z e^{x yz})

Treat

x, y

as constants

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

= 3 (1 \cdot e^{x yz} + e^{x yz} x yz)

Simplify

= 3 (e^{z x y} + e^{z x y} z x y)

\frac{d ^{3}}{d x ^{3}} (sin (3 x))

\int - 4 x ln (x) d x

(ln (x))^{2}

\frac{d}{d x} (\frac{- x sin ( x ) - cos ( x )}{x ^{2}})

\int_{1}^{2} x \cdot ln (x) d x

What is (\partial)/(\partial z)(3ze^{xyz}) ?
The answer to (\partial)/(\partial z)(3ze^{xyz}) is 3(e^{zxy}+e^{zxy}zxy)