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Differentiate the following w.r.t. x : sin-1 (1-25x21+25x2)

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प्रश्न

Differentiate the following w.r.t. x : `sin^-1  ((1 - 25x^2)/(1 + 25x^2))`

योग
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उत्तर

Let y = `sin^-1  ((1 - 25x^2)/(1 + 25x^2))`

= `sin^-1[(1 - (5x)^2)/(1 + (5x)^2)]`
Put 5x = tanθ.
Then θ = tan–1(5x)

∴ y = `sin^-1((1 - tan^2θ)/(1 + tan^2θ))`
= sin–1(cos2θ)

= `sin^-1[sin(pi/2 - 2θ)]`

= `pi/(2) - 2θ`

= `pi/(2) - 2tan^-1(5x)`
Differentiating w.r.t. x, we get
∴ `"dy"/"dx" = "d"/"dx"[pi/2 - 2tan^-1 (5x)]`

= `"d"/"dx"(pi/2) - 2"d"/"dx"[tan^-1(5x)]`

= `0 - 2 xx (1)/(1 + (5)^2)."d"/"dx"(5x)`

= `(-2)/(1 + 25x^2) xx 5`

= `(-10)/(1 + 25x^2)`.

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Differentiation - Exercise 1.2 [पृष्ठ ३०]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 1 Differentiation
Exercise 1.2 | Q 9.09 | पृष्ठ ३०

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