Question

f(x) = 1 - cos x / x^2 + 1
Quotient rule.
f(x) = 1 - cos x
f'(x) = 1 + sin x
g(x) = x^2 + 1
g'(x) = 2x
1 + sin x (x^2 + 1) - 2x(1-cosx) / (x^2 + 1 )^2
Am I correct?

Answer 1

oops, made a mistake..

Answer 2

Yup

Answer 3

sin x (x^2 + 1) - 2x(1-cosx) / (x^2 + 1 )^2
there is no 1 +..

Answer 4

Not Quite f'(x) should just be Sin(x)

Answer 5

But otherwise that is right.

Answer 6

thanks.

Answer 7

\[f'\left( \frac{ u }{ v } \right)=\frac{ vu'-uv' }{v ^{2} }\]

Answer 8

\[f'\left( \frac{ 1-\cos x }{ x ^{2}+1 } \right)=\frac{ \sin x \left( x ^{2}+1 \right)-2x \left( 1-\cos x \right) }{\left( x ^{2} +1 \right)^{2} }\]
you are absolutely correct.