Question

Question 11: Find dy/dx : y = cos¯¹(1-x² / 1+x²), 0 < x < 1

Class 12 - Math - Continuity and Differentiability

Answer 1

Refer to the attachment.
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formula used ;-
•d/dx(tan-¹x) = 1/1+x²
•cos2∅ = 1-tan²∅/1+tan²∅

Answer 2

$y = {cos}^{ - 1} ( \frac{1 - {x}^{2} }{1 + {x}^{2} } ) \\ \\ put \: \: x = tan \theta \\ \\ y = {cos}^{ - 1} ( \frac{1 - {tan}^{2} \theta }{1 + {tan}^{2} \theta } ) \\ \\ y = {cos}^{ - 1} (cos2 \theta) \\ \\ y = 2\theta \\ \\ y = 2{tan}^{ - 1} x \\ \\ \frac{dy}{dx} = \frac{2}{1 + {x}^{2} }$