# Differentiation involving Pi

1. Sep 16, 2007

### fk378

[SOLVED] Differentiation involving Pi

1. The problem statement, all variables and given/known data

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

2. Relevant 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?

3. 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]) ?

2. Sep 16, 2007

### Staff: Mentor

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

3. Sep 16, 2007

### Kurdt

Staff Emeritus
Pi is just a constant. What do you know of the derivative of $a cos(t)$ where a is a constant?

4. Sep 16, 2007

### 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?

5. Sep 16, 2007

### Staff: Mentor

Huh? Pi is a number!

6. Sep 16, 2007

### fk378

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

7. Sep 16, 2007

### Staff: Mentor

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.

8. Sep 16, 2007

### Kurdt

Staff Emeritus
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.

9. Sep 16, 2007

### fk378

Ah, I see. Thank you both :)