Question

siny=xsin(a+y)
dy/dx=?

Answer 1

I have a small doubt here..

Answer 2

is xsin(a+y) to be solved with product rule?

Answer 3

dy/dx means you take the derivative of x... since sin(a+y) does not include any x in it... no, you don't use product rule. you treat sin(a+y) as a constant coefficient

Answer 4

:o?

Answer 5

ummm.... u need to use product rule...

Answer 6

I did..

Answer 7

because y is the function of x

Answer 8

What I want to ask is..if I had ysin(a+y) then I wuldve used chain rule?

Answer 9

you only use product rule when two facots include x

for example

xsin x <-- x and sinx both have x so you use product rule

xsiny <--- siny doesn't have x so treat it as coefficient

remember that @hartnn ?

Answer 10

no, product again, because both are functions of x

Answer 11

sin y doesn't have x, right
bu since y is the function of x....

Answer 12

d/dx sin y = cos y dy/dx

Answer 13

ive done that only

Answer 14

but even WFA treats it as 0

Answer 15

WFA ?

Answer 16

wolfaram :P ALPHA

Answer 17

spelling/*

Answer 18

no...x sin(a+y) needs product rule.

Answer 19

:/

Answer 20

x cos(a+y) dy/dx + sin(a+y)

Answer 21

cos y dy/dx =x cos(a+y) dy/dx + sin(a+y)
isolate dy/dx

Answer 22

your WFA
http://www.wolframalpha.com/input/?i=siny%3Dxsin%28a%2By%29%2C++dy%2Fdx%3D%3F

Answer 23

it doesn't treat it as 0.

Answer 24

oh nvm :o

Answer 25

but still not clear why product rule..its used in product of 2 functions so x and sin(a+y) x is not a function,y is

Answer 26

x is a function of x
x^1

Answer 27

doesnt make any sense :S

Answer 28

every variable is afunction of itself then

Answer 29

you can say that.
f(x) = x^n with n=1.

Answer 30

why didnt we use chain rule for sin(a+y)

Answer 31

we actually did.

Answer 32

:o

Answer 33

sin is one function and y other right?

Answer 34

cos (a+y) d/dx(a+y)
=cos (a+y) (0+dy/dx)

Answer 35

yes.

Answer 36

so I have to treat x&y both as function not variables but other variable like abcd as constants(0) ?

Answer 37

when differentiating wrt x

Answer 38

\[\frac{d}{dx}xsin(a+y) \]\[=sin(a+y) \frac{d}{dx}(x) + x\frac{d}{dx}sin(a+y)\]\[=sin(a+y) + x[cos(a+y)\frac{d}{dx}(a+y)]\]\[=sin(a+y) + xcos(a+y)\frac{dy}{dx}\]

Answer 39

here since y is the function of x, we treat it as different function.
if a is function of x, then a is also function..... if a is independent of x, then a is constant.

Answer 40

clear!

Answer 41

:)