What is the derivative of e 5 ?

Question

What is the derivative of             e      5      ?

abuhishcy · Accepted Answer

Here are three ways to see that the derivative is 0:
The power rule and chain rule

\frac{d}{d x} (u^{5}) = 5 u^{4} \frac{d}{d x} (u)

In this case

u = e

is a constant, then we get:

\frac{d}{d x} (e^{5}) = 5 e^{4} \frac{d}{d x} (e) = 5 e^{4} \cdot 0 = 0

Exponential function and chain rule

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

In this case

u = 5

is a constant, so we get:

\frac{d}{d x} (e^{5}) = e^{5} \frac{d}{d x} (5) = e^{5} \cdot 0 = 0

e^{5}

is a constant

e \approx 2.7

, then

e^{5}

is s a number close to

{2.7}^{5}

.
The derivative of that number (a constant) is 0

\frac{d}{d x} (e^{5}) = 0

This is a lot like asking for the derivative of

2^{5}

which is clearly the same as the derivative of 32 which is 0.
The constant e causes confusion until a student gets comfortable with the fact that e is just some number.

What is the derivative of e^5?

Answered question

Answer & Explanation

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