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

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 ?

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 ?

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

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

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

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.

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