why-d-dz-e-z-e-z-why-dose-not-de-z-dz-de-z-dz-e-z-z-

Question Number 215918 by issac last updated on 21/Jan/25

why \frac{d}{d z} e^{z} = e^{z} ? ?

why dose not \frac{d e^{z}}{d z} = \frac{d e^{z}}{d z} = \frac{e^{z}}{z} ? ? ?

Answered by Frix last updated on 21/Jan/25

You mean generally \frac{d}{d x} f (x) = \frac{f (x)}{x} ?

Answered by mahdipoor last updated on 21/Jan/25

The symbol d here is an operator :

\frac{d}{d z} e^{z} \equiv \frac{e^{z + Δ z} - e^{z}}{Δ z} w h e n (Δ z \to 0)

whose name is derivative

n o t m e a n :

\frac{d}{d z} e^{z} = \frac{d \times e^{z}}{d \times z}

Answered by MathematicalUser2357 last updated on 29/Mar/25

You maybe forgot the notation of derivatives .

The derivative notations are : \frac{d y}{d x}, \frac{d}{d x} y, y^{'}, etc . (Derivative notation is marked blue)

Solving it with your derivative skills with that notation you forgot :

\frac{d}{d z} e^{z} = e^{z} .

If you {didn}^{'} t forgot the notation of derivatives,

You maybe forgot the first principle of derivatives .

If you {didn}^{'} t forgot that, you thinked \frac{d}{d z} e^{z} as an Algebra question .

Please, let that notation go to your mind .