1018
  • 1018
find y' : y=sin(x+y)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
You just have to differentiate both sides of the equation with respect to x \[\frac{d}{dx}(y)=\frac{d}{dx}(\sin(x+y))\] Left side becomes simply derivative of y with respect to x, for the right side u must use chain rule Alternatively you can separate the variables \[\sin^{-1}y=x+y\] \[\sin^{-1}(y)-y=x\] Either way you'll have to differentiate both sides of the equation, you can't just reduce the equation into a form of \[y=f(x)\] Such forms where you can't express y purely in terms of x are called as implicit, and we use implicit differentiation, in this method we simply differentiate the whole equation with respect to the independent variable and re arrange the dy/dx term
anonymous
  • anonymous
Does that makes sense to you?
1018
  • 1018
may i ask, is it always with respect to x? it says i need y'

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anonymous
  • anonymous
Generally it is with respect to x, most of the times you are required to find \[y'=\frac{dy}{dx}\] Besides think about it, your equation only has 2 variables, x and y, so you can only find derivative of y with respect to x or with respect to y, derivative of y with respect to y would be 1 so that's kind of meaningless, so of course u have to find derivative of y with respect to x
anonymous
  • anonymous
Anyways, try differentiation both sides of equation with respect to x, let's see where this gets you to
1018
  • 1018
ok i think i got it. ill try again if my answer would be incorrect. thanks!
anonymous
  • anonymous
Ok show me your work once you've attempted the question

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