Question

how do you find an equation that will work for finding the nth derrivative for -20cos2x?

Answer 1

Welcome to OpenStudy!!

To answer your question: Find the first several derivatives of -20cos 2x and then look for a pattern. Hint: If you begin with cos x and take the 1st, 2nd and 3rd derivatives, the next derivative (the 5th) will be cos x all over again. This pattern repeats itself.

Answer 2

I invite you to find the first 5 derivatives of -20 cos 2x. Type them below. Then we'll look for a pattern.

Answer 3

since -20 is a constant, it will be a factor in all the subsequent derivatives so in looking for the pattern you can even ignore the constant for the time being and see a pattern in the derivatives of cos(2x).
f(x) = cos(2x)
f'(x) = ?
f''(x) = ?
f'''(x) = ?
...

Answer 4

Right. So the first several derivatives will comprise a set that looks like

-20*{cos 2x, -2sin 2x... and so on }

Answer 5

sorry i only just got on and thank you mathmale..im kinda lost.. i did find the first five derrivatives cos(2x), -2sin(2x),-4cos(2x),8sin(2x),16cos(2x).. I've noticed a pattern im not sure if this is it but the first no. doubles and it also goes pos,pos,neg,neg..then repeating.?