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

The answer to (\partial)/(\partial z)(2xz^3e^{y^2}) is 6e^{y^2}xz^2

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

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

= 2 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}

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

Simplify

= 6 e^{y^{2}} x z^{2}

f (x) = t^{4} cos (t)

\int_{5}^{9} x^{2} d x

x \to 2 lim (2 x + 6)

5 - x^{2}, 17 - 7 x

\int c t d t

What is (\partial)/(\partial z)(2xz^3e^{y^2}) ?
The answer to (\partial)/(\partial z)(2xz^3e^{y^2}) is 6e^{y^2}xz^2