How do you use implicit differentiation to find dy/dx given #xy+y=sinx#?

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Answer 1 · 2016-12-02T08:55:06

#(dy)/(dx)=(cosx-y)/(x+1)#

#d/(dx)(xy+y)=d/(dx)(sinx)#

#d/(dx)(xy)+d/(dx)(y)=d/(dx)(sinx)#

Now differentiate using the product rule on the first term.

#y+x(dy)/(dx)+(dy)/(dx)=cosx#

Then rearrange for #" "(dy)/(dx)#

#(dy)/(dx)(x+1)=cosx-y#

#(dy)/(dx)=(cosx-y)/(x+1)#