What is (\partial)/(\partial y)(4ze^{xyz}) ?

The answer to (\partial)/(\partial y)(4ze^{xyz}) is 4e^{zxy}z^2x

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(\partial)/(\partial y)(4ze^{xyz})

\frac{\partial}{\partial y} (4 z e^{x yz})

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

Solution steps

\frac{\partial}{\partial y} (4 z e^{x yz})

Treat

z, x

as constants

Take the constant out:

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

= 4 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

= 4 z e^{x yz} z x

Simplify

4 z e^{x yz} z x : 4 e^{z x y} z^{2} x

= 4 e^{z x y} z^{2} x

x \to - 9 - lim (\frac{- 6 x}{x + 9})

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

x = 28 - 7 y^{2}, x = 7 y^{2} - 28

\frac{d y}{d x} = - y^{2}

\frac{d}{d x} (- 5 csc (x) + sec (x))

What is (\partial)/(\partial y)(4ze^{xyz}) ?
The answer to (\partial)/(\partial y)(4ze^{xyz}) is 4e^{zxy}z^2x