What is (\partial)/(\partial y)(8ze^{xyz}) ?

The answer to (\partial)/(\partial y)(8ze^{xyz}) is 8e^{zxy}z^2x

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(\partial)/(\partial y)(8ze^{xyz})

\frac{\partial}{\partial y} (8 z e^{x yz})

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

Solution steps

\frac{\partial}{\partial y} (8 z e^{x yz})

Treat

z, x

as constants

Take the constant out:

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

= 8 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

= 8 z e^{x yz} z x

Simplify

8 z e^{x yz} z x : 8 e^{z x y} z^{2} x

= 8 e^{z x y} z^{2} x

\frac{d}{d x} ((9 x^{2} + 8) (3 x + x))

\int_{2}^{4} \frac{6 + x ^{2}}{x ^{3}} d x

y = ln (9 x^{2} + 5 y^{2})

x \to \infty lim (ln (7 x + 1) - ln (4 x + 1))

\int_{0}^{5} 25 - x^{2} d x

What is (\partial)/(\partial y)(8ze^{xyz}) ?
The answer to (\partial)/(\partial y)(8ze^{xyz}) is 8e^{zxy}z^2x