What is (\partial)/(\partial x)(2ze^{xyz}) ?

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

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(\partial)/(\partial x)(2ze^{xyz})

\frac{\partial}{\partial x} (2 z e^{x yz})

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

Solution steps

\frac{\partial}{\partial x} (2 z e^{x yz})

Treat

z, y

as constants

Take the constant out:

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

= 2 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

= 2 z e^{x yz} zy

Simplify

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

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

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\int_{- 6}^{5} x^{2} - 3 x - 4 d x

cos^{2} (x)

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