What is (\partial)/(\partial z)(x^2e^{yz}) ?

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

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

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

x^{2} e^{yz} y

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

\frac{\partial}{\partial x} (sin (z) cos (x y))

x \to 0 lim (\frac{x ^{3} + 5 x}{x})

\int_{0}^{x} \frac{1}{t ^{2} - 25} d t

y^{^{'}} = y + 3 t e^{t}, y (0) = 4

x \to 3 lim (x - 8)

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