Behavior of e constant in exponents

[mathor345]

Homework Statement

differentiate

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

Homework Equations

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?

 

[SammyS]

Yes. That's correct for u being a constant.

 

[Char. Limit]

Homework Statement

differentiate

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

Homework Equations

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.

 

[mathor345]

Thank you.

 

[Mark44]

Homework Statement

differentiate

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

Homework Equations

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 = t^{5 - e}
==> dy/dt = (5 - e)t^{5 - e - 1} = (5 - e)t^{4 - e}