Find the derivatives of the following: tan-1(cosx+sinxcosx-sinx) - Mathematics

Find the derivatives of the following:

`tan^-1 ((cos x + sin x)/(cos x - sin x))`

Sum

Let y = `tan^-1 ((cos x + sin x)/(cos x - sin x))`

y = `tan^-1 ((cos x(1 + (sinx)/(cosx)))/(cos x(1 - (sin x)/(cos x))))`

y = `tan^-1 ((1 + tanx)/(1 - tanx))`

= `tan^-1 ((tan pi/4 + tan x)/(1 - tan pi/4 * tan x))`

= `tan^-1 (tan (pi/4 + x))`

y = `pi/4 + x`

`("d"y)/("d"x)` = 0 + 1

`("d"y)/("d"x)` = 1

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Differentiation Rules

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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.4 [Page 176]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 18 | Page 176

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