What is (\partial)/(\partial z)(y^2ze^z) ?

The answer to (\partial)/(\partial z)(y^2ze^z) is y^2(e^z+e^zz)

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(\partial)/(\partial z)(y^2ze^z)

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

y^{2} (e^{z} + e^{z} z)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = z, g = e^{z}

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

\frac{\partial}{\partial z} (z) = 1

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

= y^{2} (1 \cdot e^{z} + e^{z} z)

Simplify

= y^{2} (e^{z} + e^{z} z)

\frac{\partial}{\partial x} ((x^{2} + y^{2} + z^{2})^{- 0.5})

\int (sec (x) \cdot tan (x)) d x

y^{^{'}} + k y = 0

f (x) = (x^{5} - x^{3} + 3)^{4}

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 12 y = 0

What is (\partial)/(\partial z)(y^2ze^z) ?
The answer to (\partial)/(\partial z)(y^2ze^z) is y^2(e^z+e^zz)