`tan(x + y) = x, (0,0)` Find `dy/dx` by implicit differentiation and evaluate the derivative at the given point.

Textbook Question

Chapter 2, 2.5 - Problem 27 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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`tan(x+y) = x`

`or, sec^2(x+y)*[1 + (dy/dx)] = 1`

`or, dy/dx = [1-sec^2(x+y)]/{sec^2(x+y)}`

` `

``Now, dy/dx at (0,0) we get

`dy/dx = {1-sec^2(0+0)}/{sec^2(0+0)}`

`or, dy/dx = (1-1)/1 = 0`

``

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