How do I differentiate an equation involving pi?

[fk378]

[SOLVED] Differentiation involving Pi

Homework Statement

Differentiate sin(t) + (pi)cos(t)

Homework Equations

Am I supposed to leave pi alone and just solve for the cos and sin parts? Or do I get f'(x) of pi as well?

The Attempt at a Solution

I know that f'(x) of sin(t) = cos(t)
Now what do I do with the (pi)cos(t) part? Do I say that the slope of pi is zero, therefore the derivative of (pi)cos(t) is 0, then the answer would be just sin(t) for the whole equation.

OR

Leave pi there, and have f'(x) of cos(t)= -sin(t) so that would make: cos(t) + (pi)(-sin[t]) ?

 

[Doc Al]

pi is a constant, so treat it like any other number. What's the derivative of 5x? Of pi*x?

 

[Kurdt]

Pi is just a constant. What do you know of the derivative of [itex] a cos(t) [/itex] where a is a constant?

 

[fk378]

Interesting way to put it. So is that what pi will be in most differentiation cases? How will you know if they are referring to pi as the radian in which the slope = 0?

 

[Doc Al]

Huh? Pi is a number!

 

[fk378]

Yes, but Pi is also a radian measure of 180 degrees.

 

[Doc Al]

Yes, but Pi is also a radian measure of 180 degrees.

True--the number of radians in 180 degrees equals pi. Pi is also the number of square meters within a circle who's radius is one meter. And many other things. But in all cases, pi is just a pure number--and that's all you care about when differentiating an expression that contains pi.

 

[Kurdt]

That would only matter if pi was the argument of one of the trig functions, which it is not. It is merely a number multiplying the function.

 

[fk378]

Ah, I see. Thank you both :)