Question

Deriviation of cos^-1[(1+x)/2]^1/2 ??​

Answer 1

Answer:

[tex] - \frac{1}{2 \sqrt{1 - {x}^{2} } [/tex]

Step-by-step explanation:

$\frac{d}{dx} ( {cos}^{ - 1} \sqrt{ \frac{1 + x}{2} } ) \\ \\ let \: x = cos \: 2y \\ \\ \frac{d}{dx} ( {cos}^{ - 1} \sqrt{ \frac{1 + cos \: 2y}{2} } )\\ \\ \frac{d}{dx} ( {cos}^{ - 1} \sqrt{ \frac{2 {cos}^{2}y }{2} }) \\ \\ \frac{d}{dx} ( {cos}^{ - 1} \sqrt{ {cos}^{2}y } )\\ \\ \frac{d}{dx} ( {cos}^{ - 1} cos \: y ) \\ \\ \frac{d}{dx} (y) \\ \\ \frac{d}{dx} ( \frac{1}{2} {cos}^{ - 1} x) \\ \\ \frac{1}{2} \times ( - \frac{1}{ \sqrt{1 - {x}^{2} } } )$

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