dont quite understand what this is doing/asking

[Sarahisme]

hey everyone

 

i dont really understand this example in my text book, i've never seen anything asked like this before....

 

anyways if someone could please explain what they are doing, it would be greatly appreciated

 

 

Sarah

[Sarahisme]

oops, that picture is rather big, lol wasnt meant to be

 

sorry bout that peoples

[Dave]

Basically, it wants you to apply the chain rule for differentiation to an arbitrary function f. For example, when you want to work out the derivative of [math]\sin(x^2)[/math], you just use the chain rule to calculate it - i.e:

 

[math]\frac{d}{dx}\sin(x^2) = 2x \cdot \cos(x^2)[/math]

 

Same kind of thing here, only using a general function instead of a specific one.

[Sarahisme]

umm yeah i still dont completely understand....

 

if you have the time could you please explain part a) ??

 

Thanks

 

Sarah

 

p.s thanks for replying to my other question too

[Dave]

Sure - I'll use the same notation in the question. Here's the chain rule for differentiation:

 

If F(x) = f(g(x)) then: F'(x) = f'(g(x)).g'(x)

 

In this case, we have F(x) = f(3x), so g(x) = 3x and f is just some function. g'(x) = 3, so by the chain rule, we must have that:

 

[math]\frac{d}{dx} f(3x) = 3f'(3x)[/math]

 

As an example, take f = sin:

 

[math]\frac{d}{dx} \sin(3x) = 3\cos(3x)[/math]

 

Hope this helps.