Differentiation help

[Spitfir3]

Hey guys,

Right, i'm doing some work on differentiation but we've only done two classes on it so far so i'm still on the basics.

I'm having a bit of a trouble with the principles and general ideas I think... for example, could someone just clarify this:

A derivative of a function is the average rate of change of that function ?

I've got a question here, if y = sin x + cos x, find dy/dx.. no problems with that = cos x - sin x... but then it asks me to find the derivative of y at x = pi/2 rads / 90 degrees...

Is that asking for me to find the instantaneous rate of change of the function at the point x = 90 degrees?

Wolfram suggests -1 which is just plugging in 90 for the 2 x's... is it as simple as that?

Also, how does one notate that in an answer? Would it be dy/dx = -1?

This brings me to my last question, one of the questions is asked:

d/dx ( (cube rt x) + 4 * (fifth rt x) )

Is that just saying y = ( (cube rt x) + 4 * (fifth rt x) ) , find dy/dx of that function?

I can't get my head round that bit

Cheers guys

 

[Spitfir3]

Yes! Excellent, thanks so much guys Just what I wanted

One thing though, f'(x) - what's the superscript line supposed to notate? First derivative of that function?

Cheers!