What is (\partial)/(\partial z)(3xz^3e^{y^2}) ?

The answer to (\partial)/(\partial z)(3xz^3e^{y^2}) is 9e^{y^2}xz^2

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(\partial)/(\partial z)(3xz^3e^{y^2})

\frac{\partial}{\partial z} (3 x z^{3} e^{y^{2}})

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

Solution steps

\frac{\partial}{\partial z} (3 x z^{3} e^{y^{2}})

Treat

x, y

as constants

Take the constant out:

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

= 3 x e^{y^{2}} \frac{\partial}{\partial z} (z^{3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 3 x e^{y^{2}} \cdot 3 z^{3 - 1}

Simplify

= 9 e^{y^{2}} x z^{2}

\frac{\partial}{\partial z} (x z + x yz)

\int (x^{11} e^{x^{12}}) d x

\int \frac{3 x ^{2} + 2}{x ^{2}} d x

2 x + y^{2} = 8, x

\frac{\partial}{\partial y} (sin (y))

What is (\partial)/(\partial z)(3xz^3e^{y^2}) ?
The answer to (\partial)/(\partial z)(3xz^3e^{y^2}) is 9e^{y^2}xz^2