What is the first d/(dz)(e^{xz}) ?

The first d/(dz)(e^{xz}) is e^{xz}x

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d/(dz)(e^{xz})

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

e^{x z} x

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= e^{x z} x

e^{- x + 1} x - 2 e^{- x + 1}

f (x) = \frac{5}{x}, (- 4, - \frac{5}{4})

- \frac{x ^{8}}{y ^{8}}

x^{2} - 4 x, x + 6

\int \frac{31}{31 + e ^{x}} d x