`sin(x) = x(1 + tan(y))` Find `dy/dx` by implicit differentiation.

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Chapter 2, 2.5 - Problem 13 - Calculus of a Single Variable (10th Edition, Ron Larson).
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gsarora17 | (Level 2) Associate Educator

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`sin(x)=x(1+tan(y))`

Differentiating both sides with respect to x,

`cos(x)=xd/dx(1+tan(y))+(1+tan(y))d/dx(x)`

`cos(x)=x(sec^2(y) dy/(dx))+1+tan(y)`

`xsec^2(y) dy/(dx)=cos(x)-tan(y)-1`

`dy/dx=(cosx-tany-1)/(xsec^2y)`

`dy/dx=(cos^2(y)(cos(x)-tan(y)-1))/x`

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