Basic derivative, understanding a question.

**Kakariki** · March 30th 2010, 01:06 AM

Hey,

The derivative of $t e^3$ is $e^3$ . I do not understand why. The answer in my text says that the t is a constant. However, I do not understand how to tell when something is a constant, and when something is not.

Originally in this problem I used the chain rule, and found the solution to be
$(1)(e^3) + (t)(e^3)$
$= e^3 + t e^3$
which is not the answer.

I am looking for an explanation, in plain english please.

Thank you!

**Prove It** · March 30th 2010, 01:36 AM

Originally Posted by Kakariki

Hey,

The derivative of $t e^3$ is $e^3$ . I do not understand why. The answer in my text says that the t is a constant. However, I do not understand how to tell when something is a constant, and when something is not.

Originally in this problem I used the chain rule, and found the solution to be
$(1)(e^3) + (t)(e^3)$
$= e^3 + t e^3$
which is not the answer.

I am looking for an explanation, in plain english please.

Thank you!

Actually, $e^3$ is a constant. $t$ is a variable.

So $\frac{d}{dx}(e^3 t) = \frac{d}{dx}(e^3 t^1)$

$= 1e^3 t^0$

$= e^3$ .

**mathemagister** · March 30th 2010, 01:39 AM

Originally Posted by Kakariki

Hey,

The derivative of $t e^3$ is $e^3$ . I do not understand why. The answer in my text says that the t is a constant. However, I do not understand how to tell when something is a constant, and when something is not.

Originally in this problem I used the chain rule, and found the solution to be
$(1)(e^3) + (t)(e^3)$
$= e^3 + t e^3$
which is not the answer.

I am looking for an explanation, in plain english please.

Thank you!

$t$ is not the constant. $e^3$ is the constant. Remember, $e$ is just a number (constant, not a variable). Any constant cubed will also be a constant.

Just as the derivative of $4t$ will be $4$ : the derivative of $e^3t$ will be $e^3$ .

Does that help?

Mathemagister

**Kakariki** · March 30th 2010, 02:01 AM

OH!!!!!!!!!! That makes complete sense. I was under the impression that t would be a constant, and it just didn't make any sense to me at all. e^3 being a constant does make sense though! The graph of te^3 would be a line, would it not? Then the derivative would be e^3 (a horizontal line).

Wow, I was just looking at it wrong.

THANK YOU!

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