Question

Differentiate the following:

Answer 1

\[\LARGE f(x)=(x+x^{-1})^3\]

Answer 2

\(\Huge \color{green}{(\frac{x^2+1}{x})^3}=(x+x^-1)^3\)

Answer 3

\(\Huge \text{let} \frac{x^2+1}{x} =u\)

Answer 4

then u wud have
\(\Huge (u^3)'=3u'(u)^2\)

Answer 5

Why not do \[
\sqrt[3]{f(x)} = x+x^{-1}
\]And then differentiate?

Answer 6

its to power 3 not 2

Answer 7

You would get:\[
[f(x)]^{-2/3}f'(x) = 1+\ln(x)
\]

Answer 8

So \[
f'(x) = \left(1+\ln(x)\right)\left(\left(x+x^{-1}\right)^{3}\right)^{2/3}
=\left(1+\ln(x)\right)\left(x+x^{-1}\right)^{2}
\]

Answer 9

i wud get
3(1-x^-2)(x+x^-1)^2

Answer 10

im a bit confused nw :o

Answer 11

Hmmm, maybe I differentiated wrong.

Answer 12

i dnt know were did u came with the ln formula its derevative not integral

even if u let it
f(x)=(x+x^-1)^3
let u =x+x^-1
then u'=1-x^-2
and (u^3)'=3u'u^2=3(1-x^-2)(x+x^-1)^2

Answer 13

probably should be \(x^{-2}\) instead of \(\ln(x)\)

Answer 14

(x^-1)'=-x^-2

(ln x)'=1/x

:o

Answer 15

This is so easy, but I can't help my student Luigi.