Question

y = sin^{-1}(2x/1+x^{2}) dy/dx ज्ञात कीजिए

Answer 1

dy/dx = 2/(1 + x²)  यदि y = Sin⁻¹(2x/(1 + x²))

Step-by-step explanation:

dy/dx ज्ञात कीजिए

y = Sin⁻¹(2x/(1 + x²))

=> Siny  =  2x/(1  + x²)

=> Cosydy/dx  =  (2x (-1) /(1 + x²)² ) * 2x   +  2/(1 + x²)

=> Cosydy/dx  =  (-4x²  + 2(1 + x²) )/(1 + x²)²

=> Cosydy/dx  =  (2 - 2x²) )/(1 + x²)²

Siny  =  2x/(1  + x²)

=> Cosy  = √ (1 - Sin²y)  = √ (1   -  4x²/(1 + x²)²

= √(1 + x⁴ + 2x² - 4x²)/(1 + x²)²

= √(1 - x²)²/(1 + x²)²

= (1 - x²)/(1 + x²)

Cosydy/dx  =  (2 - 2x²) )/(1 + x²)²

=> (1 - x²)/(1 + x²)dy/dx  = 2(1 - x²) )/(1 + x²)²

=> dy/dx = 2/(1 + x²)

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