What is (\partial)/(\partial z)(yze^{xz}) ?

The answer to (\partial)/(\partial z)(yze^{xz}) is y(e^{zx}+e^{zx}zx)

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(\partial)/(\partial z)(yze^{xz})

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

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

Solution steps

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

Treat

y, x

as constants

Take the constant out:

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

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

Apply the Product Rule:

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

f = z, g = e^{x z}

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

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

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

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

Simplify

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

\frac{d y}{d x} = \frac{3 x ^{2} - 1}{2 y}

\frac{d}{d x} (\frac{1}{2} csc (\frac{x}{4}))

\frac{d y}{d x} = \frac{( x ^{2} + 3 y ^{2} )}{2 x y}

ln (x^{2} + 1) + e^{- x^{2}}

\frac{100}{x}

What is (\partial)/(\partial z)(yze^{xz}) ?
The answer to (\partial)/(\partial z)(yze^{xz}) is y(e^{zx}+e^{zx}zx)