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

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

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

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

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

Solution steps

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

Treat

z, x

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 6 z e^{x yz} z x

Simplify

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

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

\frac{1 + x}{1 - x}

\int_{- 1}^{2} \frac{4}{x ^{3}} d x

n = 0 \sum \infty \frac{4}{7 ^{n - 1}}

\frac{\partial}{\partial x} (- sin (x y))

y = 0.5 x - 3

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