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1018
 one year ago
find y' :
y=sin(x+y)
1018
 one year ago
find y' : y=sin(x+y)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You 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
 one year ago
Best ResponseYou've already chosen the best response.0Does that makes sense to you?

1018
 one year ago
Best ResponseYou've already chosen the best response.0may i ask, is it always with respect to x? it says i need y'

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Generally 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
 one year ago
Best ResponseYou've already chosen the best response.0Anyways, try differentiation both sides of equation with respect to x, let's see where this gets you to

1018
 one year ago
Best ResponseYou've already chosen the best response.0ok i think i got it. ill try again if my answer would be incorrect. thanks!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok show me your work once you've attempted the question
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