What is (\partial)/(\partial y)(xye^{yz}) ?

The answer to (\partial)/(\partial y)(xye^{yz}) is x(e^{yz}+e^{yz}yz)

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(\partial)/(\partial y)(xye^{yz})

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the Product Rule:

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

f = y, g = e^{yz}

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

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

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

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

Simplify

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

\int 9 e^{u} d u

f (x) = x^{2} + x, (7, 56)

\frac{\partial}{\partial x} (\frac{7 x - 4 y}{7 x + 4 y})

\int t \cdot e^{- s t} d t

\frac{3}{4 ( s + 1 ) ^{2} - 16}

What is (\partial)/(\partial y)(xye^{yz}) ?
The answer to (\partial)/(\partial y)(xye^{yz}) is x(e^{yz}+e^{yz}yz)