What is (\partial)/(\partial z)(y^2e^{xyz}) ?

The answer to (\partial)/(\partial z)(y^2e^{xyz}) is e^{yxz}y^3x

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(\partial)/(\partial z)(y^2e^{xyz})

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

e^{y x z} y^{3} x

Solution steps

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

Treat

y, x

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

y^{2} e^{x yz} y x : e^{y x z} y^{3} x

= e^{y x z} y^{3} x

\int_{1}^{\infty} \frac{1}{x ^{2} + 4} d x

\frac{\partial}{\partial x} (x^{2} + x y + y^{2} - 6 x + 2)

\int \frac{e ^{2} x}{4 + e ^{4} x} d x

\frac{d y}{d x} = \frac{( 2 x + 1 )}{2 y}

9 x (2 x^{2} + 1)

What is (\partial)/(\partial z)(y^2e^{xyz}) ?
The answer to (\partial)/(\partial z)(y^2e^{xyz}) is e^{yxz}y^3x