Question

How to solve for the derivative of (1/X+1) +X +1

Answer 1

\[\frac{ 1 }{ X+1 } +X +1\]

Answer 2

you know how to differentiate x+1?

Answer 3

for the first term you can use quotient rule
for the second term you can use power rule
for the third term you can use constant rule

Answer 4

is the constant rule where it stays the same?
so there are three terms right, i don't understand why the second term uses power wouldn't it be the f(x) +or- g(x)?

Answer 5

HI!!

Answer 6

\[\frac{d}{dx}(constant)=0 \]

Answer 7

\[\frac{d}{dx}(\frac{1}{x+1}+x+1) \\ =\frac{d}{dx}(\frac{1}{x+1})+\frac{d}{dx}(x)+\frac{d}{dx}(1)\]

Answer 8

you could actually write 1/(x+1) as (x+1)^(-1) and forget about quotient if you prefer

Answer 9

you could look at the 2nd and 3rd as one ... if you want
and ask yourself what is the slope of the line y=x+1

Answer 10

okay i understand now thank you i think i might skip the quotient and implement a negative power like you said. thanks

Answer 11

did you want to write what you have so I can check it?

Answer 12

sure thanks \[\frac{ 1}{ x+1 } +x+1 \]

Answer 13

\[(x+1)^{-1}\]

Answer 14

i meant \[(x+1)^{-1}+1+1\]

Answer 15

\[\frac{1}{x+1}+x+1=(x+1)^{-1}+x+1\]

Answer 16

then \[-1(x+1)^{-2} +1+1\]

Answer 17

whait i thought the x became a 1 because of the power rule?

Answer 18

\[\frac{d}{dx}(\frac{1}{x+1}+x+1) \\ \frac{d}{dx}(x+1)^{-1}+\frac{d}{dx}x+\frac{d}{dx}1 \\ -1(x+1)^{-2}+1+0\]

Answer 19

ohhh i seee

Answer 20

dx/dx is 1 but d(constant)/dx=0

Answer 21

the answer is supposed to be \[\frac{ x ^{2}+2x }{ (x+1)^{2} }\]
i can see how the bottom works out but no the top

Answer 22

\[\frac{d}{dx}(\frac{1}{x+1}+x+1) \\ \frac{d}{dx}(\frac{1}{x+1})+\frac{d}{dx}(x) +\frac{d}{dx}(1) \\ \frac{d}{dx}(x+1)^{-1} +1+0 \\ -1(x+1)^{-2}+1 \\ -\frac{1}{(x+1)^2}+1\]
try combining the fractions

Answer 23

\[\frac{-1}{(x+1)^2}+1=...\]

Answer 24

remember you can write 1 as (x+1)^2/(x+1)^2
this will allow you have the same denominator so your can write the two fractions as one

Answer 25

you can try wolframalpha.com they also show great explanations