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DLSBest ResponseYou've already chosen the best response.0
I have a small doubt here..
 one year ago

DLSBest ResponseYou've already chosen the best response.0
is xsin(a+y) to be solved with product rule?
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
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
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
ummm.... u need to use product rule...
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
because y is the function of x
 one year ago

DLSBest ResponseYou've already chosen the best response.0
What I want to ask is..if I had ysin(a+y) then I wuldve used chain rule?
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
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 ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
no, product again, because both are functions of x
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
sin y doesn't have x, right bu since y is the function of x....
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
d/dx sin y = cos y dy/dx
 one year ago

DLSBest ResponseYou've already chosen the best response.0
but even WFA treats it as 0
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
no...x sin(a+y) needs product rule.
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
x cos(a+y) dy/dx + sin(a+y)
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
cos y dy/dx =x cos(a+y) dy/dx + sin(a+y) isolate dy/dx
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
your WFA http://www.wolframalpha.com/input/?i=siny%3Dxsin%28a%2By%29%2C++dy%2Fdx%3D%3F
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
it doesn't treat it as 0.
 one year ago

DLSBest ResponseYou've already chosen the best response.0
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
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
x is a function of x x^1
 one year ago

DLSBest ResponseYou've already chosen the best response.0
every variable is afunction of itself then
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
you can say that. f(x) = x^n with n=1.
 one year ago

DLSBest ResponseYou've already chosen the best response.0
why didnt we use chain rule for sin(a+y)
 one year ago

DLSBest ResponseYou've already chosen the best response.0
sin is one function and y other right?
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
cos (a+y) d/dx(a+y) =cos (a+y) (0+dy/dx)
 one year ago

DLSBest ResponseYou've already chosen the best response.0
so I have to treat x&y both as function not variables but other variable like abcd as constants(0) ?
 one year ago

DLSBest ResponseYou've already chosen the best response.0
when differentiating wrt x
 one year ago

RolyPolyBest ResponseYou've already chosen the best response.0
\[\frac{d}{dx}xsin(a+y) \]\[=sin(a+y) \frac{d}{dx}(x) + x\frac{d}{dx}sin(a+y)\]\[=sin(a+y) + x[cos(a+y)\frac{d}{dx}(a+y)]\]\[=sin(a+y) + xcos(a+y)\frac{dy}{dx}\]
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
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.
 one year ago
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