Question

whats the derivative of y=sin(x+y)

Answer 1

do i use the chain rule?

Answer 2

yes

Answer 3

and don't forget the \(y'\) when you do it

Answer 4

so cos(x+y)x 1 x y'

Answer 5

\[ y=\sin(x+y)\]
\[y'=\cos(x+y)\times (1+y')\]

Answer 6

now you have to solve for \(y'\)

Answer 7

hope it is clear about the \(1+y'\) part

Answer 8

how do i solve for y'?

Answer 9

do i divide cos(x+y) ?

Answer 10

should i foil?

Answer 11

i would multiply first and get \[y'=\cos(x+y)+y'\cos(x+y)\] then maybe subtract at the \(y'(\cos(x+y')\) term and get
\[y'-\cos(x+y)=\cos(x+y)\]

Answer 12

there is no "foil" here just one multiplication

Answer 13

i made a typo, last line should be
\[y'-y'\cos(x+y)=\cos(x+y)\]

Answer 14

then factor out the \(y'\) term on the left and get
\[y'(1-\cos(x+y))=\cos(x+y)\] and finally divide

Answer 15

get
\[y'=\frac{\cos(x+y)}{1-\cos(x+y)}\]

Answer 16

awsome, thanks

Answer 17

yw

Answer 18

can you also help me with \[h(x)=x \sqrt{x+1}\]

Answer 19

i used the product rule, but im not getting the right answer

Answer 20

sure

Answer 21

use
\[(fg)'=f'g+g'f\] with
\[f(x)=x, f'(x)=1, g(x)=\sqrt{x+1}, g'(x)=\frac{1}{2\sqrt{x+1}}\]

Answer 22

you good from there?

Answer 23

yeahi got 1 times \[\sqrt{x+1} + x \times 1/2\sqrt{x+1}\]

Answer 24

ok looks good
then you can add if you like

Answer 25

so the answer is x+\[\sqrt{x+1}/2\sqrt{x+1}?\]

Answer 26

with teh plus x on top

Answer 27

\[\sqrt{x+1}+\frac{x}{2\sqrt{x+1}}=\frac{2(x+1)+x}{2\sqrt{x+1}}\]
\[=\frac{3x+2}{\sqrt{x+1}}\]

Answer 28

algebra steps clear?

Answer 29

the final answer supposedly has a 2 on the bottom

Answer 30

if you want to add \(\sqrt{x+1}+\frac{x}{2\sqrt{x+1}}\) you have to multiply the first term top and bottom by \(2\sqrt{x+1}\)

Answer 31

yeah the final answer has a 2 in the bottom, i made a typo

Answer 32

\[=\frac{3x+2}{2\sqrt{x+1}}\]

Answer 33

oh, hmm okay

Answer 34

i just feellike every problem is completely different even if i use the rules, i never understand how to go about simplifying

Answer 35

that is a problem not with the rules, but with the algebra is my guess

Answer 36

calculus is unfortunately where the algebra rubber hits the road
you have to be confident in doing the algebra, because that is really where almost all of the work is

Answer 37

are there more or are you good?

Answer 38

i think im okay for now. thanks for the help

Answer 39

yw

Answer 40

God FOIL is the death of education in mathematics.