What is (\partial)/(\partial x)(6ze^{xyz}) ?

The answer to (\partial)/(\partial x)(6ze^{xyz}) is 6e^{zxy}z^2y

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(\partial)/(\partial x)(6ze^{xyz})

\frac{\partial}{\partial x} (6 z e^{x yz})

6 e^{z x y} z^{2} y

Solution steps

\frac{\partial}{\partial x} (6 z e^{x yz})

Treat

z, y

as constants

Take the constant out:

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

= 6 z \frac{\partial}{\partial x} (e^{x yz})

Apply the chain rule:

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

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

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

= 6 z e^{x yz} zy

Simplify

6 z e^{x yz} zy : 6 e^{z x y} z^{2} y

= 6 e^{z x y} z^{2} y

y^{^{'}} = 20 - 4 y

e^{- 43 t} \cdot e^{72 t} cos (77 t)

\int 5 sin (\frac{x}{4}) d x

\frac{d}{d s} (\frac{1}{s ^{2}})

4 x^{- \frac{1}{8}}

What is (\partial)/(\partial x)(6ze^{xyz}) ?
The answer to (\partial)/(\partial x)(6ze^{xyz}) is 6e^{zxy}z^2y