Anyone got their maths hat on ?

Nomisf

Nomisf

Nomisf

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Got down to the last problem i have to solve , but in my tired state I just can't seem to fathom how it works - so if anyone could explain it would really be helpful.

I'm looking for the 2nd and 10th derivative of

Code: 
g(y) = a cos(3x)   Where 'a' is a constant

I know because of the nature of cos it repeats in some fashion , and that the 10th derivative will be (a)(something)cos(3x), but i just cant get the something.

Anyone care to explain, there's a cookie in it :D*

*No actual cookies can be provided at this time
 
To diff cos you get negative sin.
To diff negative sin you get negative cos.
To diff negative cos you get positive sin.
To diff positive sin you get positive cos.
Can you see the pattern?

To differentiate a trigonometric function you have to "diff by parts", i.e diff what you have in your brackets, multiply it by a and then change the function using the above pattern.

You can get the tenth, hundredth or a millionth derivative easily, but it's probably beyond the scope of your couse. :)
 
everytime you take the derivative with respect to x the coefficient gets multiplied by 3. Also the derivate of cos goes:

cos
-sin
-cos
sin
cos

so the second derivative is -a*(3^2)cos3x and the tenth will be -a*(3^10)cos3x.

At least I hope that's right! :)
 
Nomisf said:
Got down to the last problem i have to solve , but in my tired state I just can't seem to fathom how it works - so if anyone could explain it would really be helpful.

I'm looking for the 2nd and 10th derivative of

Code: 
g(y) = a cos(3x)   Where 'a' is a constant
Click to expand...

The 2nd and 10th derivative is 0, since g is a function of y. :rolleyes:
 
Ricochet J said:
you have to "diff by parts"
Click to expand...

I believe you got mixed up with "Integration by parts". The actual rule being used here is the "Chain rule" for differentiation.

I.e in Leibniz notation dy/dx = dy/du * du/dx

So for the case of the first derivative it would be
a * (cos u)' * u', let u = 3x
= -3a sin(3x)

and the 2nd and tenth derivatives are what were stated previously.

Hope I got that right.
 
Schoolboy error tbh ;)

Also, I love the way normal people run out screaming as soon as we pro maths guys start discussing mathematical problems :P
 
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