Find a formula of f^(n)(x), if f(x)=(4+x)^(-1).

Find the third degree polynomial Q such that Q(1)=-1, Q'(1)=1, Q''(1)=8, and Q'''(1)=18.

Suppose that f(x)=g(x)/x^3 and that g is twice differentiable. Find f'' in terms of g, g', and g''.

Thanks!

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- Jan 6th 2007, 04:31 PMasnxbbyx113Calculus n-th derivatives
Find a formula of f^(n)(x), if f(x)=(4+x)^(-1).

Find the third degree polynomial Q such that Q(1)=-1, Q'(1)=1, Q''(1)=8, and Q'''(1)=18.

Suppose that f(x)=g(x)/x^3 and that g is twice differentiable. Find f'' in terms of g, g', and g''.

Thanks! - Jan 6th 2007, 04:37 PMThePerfectHacker
- Jan 6th 2007, 07:42 PMSoroban
Hello, asnxbbyx113!

Quote:

Find a formula for , if

Start cranking out derivatives and look for a pattern . . .

Therefore: .

- Jan 6th 2007, 08:07 PMSoroban
Hello again, asnxbbyx113!

Quote:

Find the third-degree polynomial such that:

. .

Let

Then: .

Since

Since

Since

Since

Therefore: .