What is (\partial)/(\partial z)(xye^{yz}) ?

The answer to (\partial)/(\partial z)(xye^{yz}) is e^{yz}xy^2

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(\partial)/(\partial z)(xye^{yz})

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

e^{yz} x y^{2}

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x y e^{yz} y

Simplify

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

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

x \to 3 lim (∣ x - 2 ∣)

\int (2 + 2 x) d x

x \to 0 lim (\frac{cos ( \frac{1}{x} )}{x})

\int (cot (2 t))^{5} d t

f (x) = (5 x - 2)^{2}

What is (\partial)/(\partial z)(xye^{yz}) ?
The answer to (\partial)/(\partial z)(xye^{yz}) is e^{yz}xy^2