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Math Help - Implicit Differentiation

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    Implicit Differentiation

    I don't really know how to do implicit differentiation. Could you show me how to do it with the equation y-sin(xy)=x ? Thanks!
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    Quote Originally Posted by suchgreatheights View Post
    I don't really know how to do implicit differentiation. Could you show me how to do it with the equation y-sin(xy)=x ? Thanks!
    I assume the main trouble is to get \frac{d \sin (xy) }{dx} (if it isn't then I suggest you go back and review the topic and then attempt some easier questions). First make the substitution u = xy and use the chain rule:

    \frac{d \sin (xy) }{dx} = \frac{d \sin u}{du} \cdot \frac{du}{dx} = \cos u \cdot \frac{du}{dx} = \cos (xy) \cdot \frac{d (xy)}{dx}.

    I assume you can use the product rule to get \frac{d (xy)}{dx} = y + x \frac{dy}{dx} and then put it all together.
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    Ok I get that but where does the first y fit in? What would be the final answer?
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    Quote Originally Posted by suchgreatheights View Post
    Ok I get that but where does the first y fit in? What would be the final answer?
    You're meant to differentiate each term of y - \sin (xy) = x^2. I differentiated the second term for you, which I assumed was the one causing you the trouble.
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