Ti-89 titanium derivative wrong?

[cbaltar2]

Hello guys,

I tried the derivative of f[x]=Cos[x Pi]/(x+1) (Pi is the usual 2nd+Pi key). The calculator outputs:

f'[x]=-Pi/(x+1)^2*Sin[Pi/(x+1)]

when the correct derivative is

f'[x]=-Pi/(x+1)^2*Sin[x Pi/(x+1)], as you could easily check by hand or in Mathematica.

What's up with that?!

By the way, the calculator has nothing stored in variable x, and the mode is set to radians.

[kkyolpep]

Did you actually do this by hand? I put this in my calculator too and I see what you mean. So I did it by hand as well. I am not sure why it does this but do you understand why it is the real answer as you posted? Look at it like this... The d/dx of Cos(2x) is -2 Sin(2x). When solving for the one you posted about first you take the product rule like the example I said, when you take the derivative of the (Pi*x)/(x+1) you have to use quotient rule. But when the answer comes out on the calculator the X is missing in the final answer. I think you just need to look at it and realize that what is in the parenthesis in the final answer is supposed to be exactly what was in them in the first place. Guess thats why they teach us this stuff so when we plug and chug we can have an understanding of what the calculator is spitting out. My thinking is that when it starts out it is taking d/dx of the Pi*x first which equals Pi, then takes the quotient rule of Pi/(x+1) that which is where the -(Pi)/((x+1)^2) is coming from. Hope I was clear enough with what I was trying to say.

[cbaltar2]

Okay,

LOL, I got it, after re-thinking about the problem when I saw your post. Here's what's going on:

Sin[Pi/(x+1)] = Sin[Pi - Pi/(x+1)] = Sin[x Pi/(x+1)], according to basic trigonometry.

So the result d/dx[Cos[x Pi/(x+1)]] = -Pi/(x+1)^2*Sin[Pi/(x+1)] is actually correct. The reason it was confusing is that the calculator's CAS automatically does a full simplification. So heads up for manipulations of this sort of trigonometric functions.