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Math Help - Implicit Differentiation w/ sin(x)

  1. #1
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    Post Implicit Differentiation w/ sin(x)

    Hey, so I'm having trouble differentiating this problem.....


    ysin[x(squared)]=xsin[y(squared)]



    any help would be appreciated
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by CALsunshine View Post
    Hey, so I'm having trouble differentiating this problem.....


    ysin[x(squared)]=xsin[y(squared)]



    any help would be appreciated
    y\sin\left(x^2\right)=x\sin\left(y^2\right)

    You would need to apply product and chain rules when differentiating both sides!

    \frac{d}{\,dx}\left[y\sin\left(x^2\right)\right]=\frac{d}{\,dx}\left[x\sin\left(y^2\right)\right] \implies 2xy\cos\left(x^2\right)+\sin\left(x^2\right)\frac{  \,dy}{\,dx}=\sin\left(y^2\right)+2xy\cos\left(y^2\  right)\frac{\,dy}{\,dx}

    Can you take it from here and solve for \frac{\,dy}{\,dx}?

    --Chris
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  3. #3
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    yes...I can solve for dy/dx from there, thank you so much.
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