What is the d/(d{z)}({y}{z}e^{{x}{z}}) ?

The d/(d{z)}({y}{z}e^{{x}{z}}) is {y}(e^{{x}{z}}+e^{{x}{z}}{x}{z})

What is the first d/(d{z)}({y}{z}e^{{x}{z}}) ?

The first d/(d{z)}({y}{z}e^{{x}{z}}) is {y}(e^{{x}{z}}+e^{{x}{z}}{x}{z})

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\frac{d}{d z} (y z e^{x z})

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

Solution steps

\frac{d}{d z} (y z e^{x z})

Take the constant out:

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

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

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

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

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

Simplify

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

What is the d/(d{z)}({y}{z}e^{{x}{z}}) ?
The d/(d{z)}({y}{z}e^{{x}{z}}) is {y}(e^{{x}{z}}+e^{{x}{z}}{x}{z})
What is the first d/(d{z)}({y}{z}e^{{x}{z}}) ?
The first d/(d{z)}({y}{z}e^{{x}{z}}) is {y}(e^{{x}{z}}+e^{{x}{z}}{x}{z})