Get the solution to "Compute the given derivatives ddxex=? at x=e"

College
Calculus and Analysis
Differential Calculus
Derivatives

ruigE

Answered question

2021-10-17

Compute the given derivatives $\frac{d}{d x} e^{x} = ? a t x = e$

Answer & Explanation

joshyoung05M

Skilled2021-10-18Added 97 answers

Step 1
We have to find
$\frac{d}{d x} e^{x} = ? a t x = e$
Let $y = e^{x}$
Taking log on both sides, we get
$\log y = x$
Differentiate it with respect to x,
$\frac{1}{y} \frac{d y}{d x} = \frac{d}{d x} x$
$\frac{d y}{d x} = y$
$\frac{d y}{d x} = e^{x}$ ...(1)
Step 2
Put $x = e$ in (1), we get
${(\frac{d y}{d x})}_{x = e} = e^{e}$

Jeffrey Jordon

Expert2022-08-13Added 2605 answers

Answer is given below (on video)

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