Math Is Fun Forum

ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

''differentiation''

Find g'(4) given that f(4)=3 and f'(4)=-5

a) g(x) = √x.f(x)    b) g(x) = f(x)/x 

Have no idea what to do here can someone please explain, much appreciated thanks.

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"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei

ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

Re: ''differentiation''

Also.   Find a general formula for F''(x) if F(x) = xf(x) and f and f' are differentiable at x.

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"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: ''differentiation''

Find

using the chain rule. Then substitute

into the equation for

.

I’ll show how to do (a) so you can do (b) yourself.

Then you put

to get

.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: ''differentiation''

Also.   Find a general formula for F''(x) if F(x) = xf(x) and f and f' are differentiable at x.

Use the chain rule as in the previous problem. This time you differentiate twice.

Now differentiate again.

ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

Re: ''differentiation''

(b)  For n≥2, conjecture a formula for F^n'(x)   ( the nth derivative )

Would it just be  F^n'(x) = nf^(n-1)'(x) + xf^n'(x)

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"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: ''differentiation''

You're only asked to conjecture, which means you don't need to necessarily get the right answer (although in this case it looks like you have).
You just need to come up with a reasonable guess based on a pattern in the formulas you know.

Your answer fits with F(x), F'(x) and F''(x), so it's a good conjecture.

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Why did the vector cross the road?
It wanted to be normal.