# Behavior of e constant in exponents

## Homework Statement

differentiate

$$y = t^{5-e}$$

Power rule

## The Attempt at a Solution

$$u = (5 - e)$$

$$(u)t^{u - 1}$$

= $$(5 - e)t^{4-e}$$

Is this a correct usage? I'm not sure if there are any equations regarding this, but since e is a constant this should be correct right?

## Answers and Replies

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SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
Yes. That's correct for u being a constant.

Char. Limit
Gold Member

## Homework Statement

differentiate

$$y = t^{5-e}$$

Power rule

## The Attempt at a Solution

$$u = (5 - e)$$

$$(u)t^{u - 1}$$

= $$(5 - e)t^{4-e}$$

Is this a correct usage? I'm not sure if there are any equations regarding this, but since e is a constant this should be correct right?
Yeah, that'll work.

Thank you.

Mark44
Mentor

## Homework Statement

differentiate

$$y = t^{5-e}$$

Power rule

## The Attempt at a Solution

$$u = (5 - e)$$

$$(u)t^{u - 1}$$

= $$(5 - e)t^{4-e}$$

Is this a correct usage? I'm not sure if there are any equations regarding this, but since e is a constant this should be correct right?
The mechanics are all right, but you haven't made it clear what you're doing, which is finding dy/dt. Your notation isn't helpful at all, with u mixed in with y and t.

This is how I would do it:

y = t5 - e
==> dy/dt = (5 - e)t5 - e - 1 = (5 - e)t4 - e