Calc2.24

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Find the derivative of y\, with respect to x\,: \sin(xy)=x\,, where y\, is a function of x\,

We can not easily solve for y. Instead take the derivative of both sides right now using implicit differentiation. Since y\, is a function of x\,, the derivative of y\, is y'\,, not 0\,.

\cos(xy)(y+xy')=1\,

Now solve this for y'\,

y'={\frac  {1-y\cos(xy)}{x\cos(xy)}}\,


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