• DLS

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

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  • DLS

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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  • DLS
I have a small doubt here..
  • DLS
is xsin(a+y) to be solved with product rule?
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

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Other answers:

  • DLS
:o?
ummm.... u need to use product rule...
  • DLS
I did..
because y is the function of x
  • DLS
What I want to ask is..if I had ysin(a+y) then I wuldve used chain rule?
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 ?
no, product again, because both are functions of x
sin y doesn't have x, right bu since y is the function of x....
d/dx sin y = cos y dy/dx
  • DLS
ive done that only
  • DLS
but even WFA treats it as 0
WFA ?
  • DLS
wolfaram :P ALPHA
  • DLS
spelling/*
no...x sin(a+y) needs product rule.
  • DLS
:/
x cos(a+y) dy/dx + sin(a+y)
cos y dy/dx =x cos(a+y) dy/dx + sin(a+y) isolate dy/dx
your WFA http://www.wolframalpha.com/input/?i=siny%3Dxsin%28a%2By%29%2C++dy%2Fdx%3D%3F
it doesn't treat it as 0.
  • DLS
oh nvm :o
  • DLS
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
x is a function of x x^1
  • DLS
doesnt make any sense :S
  • DLS
every variable is afunction of itself then
you can say that. f(x) = x^n with n=1.
  • DLS
why didnt we use chain rule for sin(a+y)
we actually did.
  • DLS
:o
  • DLS
sin is one function and y other right?
cos (a+y) d/dx(a+y) =cos (a+y) (0+dy/dx)
yes.
  • DLS
so I have to treat x&y both as function not variables but other variable like abcd as constants(0) ?
  • DLS
when differentiating wrt x
\[\frac{d}{dx}xsin(a+y) \]\[=sin(a+y) \frac{d}{dx}(x) + x\frac{d}{dx}sin(a+y)\]\[=sin(a+y) + x[cos(a+y)\frac{d}{dx}(a+y)]\]\[=sin(a+y) + xcos(a+y)\frac{dy}{dx}\]
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.
  • DLS
clear!
:)

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