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carolm31 · May 7, 2009, 08:17 PM

okay I found that I am stuck on thes questions I solved the answer to some but have no idea if they are correct. Please please help.

okay it says:

find d/dx (1+cos2x/2) I got -2cos x sin x is that correct

d/dx 2cot ²(2x) I got cos(2x)/sin³(2x) is that correct

if f(x)=4cot x+ 3tan x then the f(pie/4) I got 2 is that correct

if f(x)=2sinx-3cosx then f(pie)=? I got 2

if y=7x² =3x and x=sint then dy/dx=? I got 14cos²t+3cos t is that correct

ebaines · May 8, 2009, 06:06 AM

For the first problem, you wrote: d/dx(1+cos2x/2)
which I interpret as:
$ \frac d {dx} (1 + \frac {cos(2x)} 2) $

The derivtive of that is -sin(2x).

However, if what you meant was:
$ \frac d {dx} (1 + \frac {cos^2 (x) } 2) $

then the derivative is close to what you have, we just differ by a factor of 2:

$ \frac d {dx} (1 + \frac {cos^2 (x) } 2) = -cos(x) sin(x) $

For the second I think you're off by a factor of -8:

$ \frac d {dx} (2 cot^2 (2x)) = 4 cot(2x) \cdot \frac {-1} {sin^2(2x) } \cdot 2 = -8 \frac {cos(2x)} {sin^3(2x)} $

For the third: remember that
$ cot(\pi/4) = \frac {cos(\pi /4)} {sin (\pi /4)} = \frac {\sqrt 2 / 2} {\sqrt 2 / 2} = 1. $

Similarly, $tan(\pi)/4$ also equals 1.

For problem 4,
$ f(\pi) = 2 sin(\pi) - 3cos(\pi) = 2(0) - 3(-1) = 3. $

I don't understand problem 5: what do you mean by: if y=7x² =3x ?

Unknown008 · May 8, 2009, 11:20 AM

I think the last one is a typo, see the equal sign on the same button as the plus sign? Then, I assume that the actual equation was y = 7x² + 3x

But then, dy/dx would be simply 14x + 3. If you want t substitute for x = sin t, then it would be 14sin(t) + 3.

Or was it y = 7t² + 3t ?

galactus · May 9, 2009, 11:15 AM

The main thing is never spell ${\pi}$ as Pie. Come on. :rolleyes:

It is the 16th letter of the Greek alphabet, not a pastry.

Unknown008 · May 9, 2009, 11:18 AM

Lol, I haven't spotted that! It's spelled as Pi :)

galactus · May 9, 2009, 11:35 AM

That jumps out at me every time I see it, and I have spotted it too often.

Here's a good one. Yesterday, I was surfing a math site and someone wanted help with a linear regression.

They were given 4 x values and 4 y values.

What they meant was x=1,2,4,5.

They wrote it as x1245. Can you believe that?

No inkling of common sense at all. In helping, I thought it was one number, 1245, and went with that.

I suppose the 'Pie' thing doesn't really matter, but I think it looks rather inane coming from someone who is studying math and should know better.

Unknown008 · May 9, 2009, 11:41 AM

Ow, how annoying! But yes, some background of the math we study is good to know, just in case. ;)