What is (\partial)/(\partial z)(xze^{yz}) ?

The answer to (\partial)/(\partial z)(xze^{yz}) is x(e^{zy}+e^{zy}zy)

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(\partial)/(\partial z)(xze^{yz})

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

x (e^{zy} + e^{zy} zy)

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the Product Rule:

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

f = z, g = e^{yz}

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

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

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

= x (1 \cdot e^{yz} + e^{yz} yz)

Simplify

= x (e^{zy} + e^{zy} zy)

y^{^{'}} = 0.23 y - 0.0005 y^{2}

\int_{0}^{60} (60 - y)^{2} d y

x y^{^{'}} + y = 3 x y

\int_{1}^{10} \frac{1}{x ^{2}} d x

x^{2} (sin (x))

What is (\partial)/(\partial z)(xze^{yz}) ?
The answer to (\partial)/(\partial z)(xze^{yz}) is x(e^{zy}+e^{zy}zy)