y = sin^{-1} (\frac{1}{2x^{2}-1}), 0
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dy/dx = - 2 / (2x² - 1) √(x² - 1) यदि y = Sin⁻¹ ( 1/ (2x² - 1))
Step-by-step explanation:
y = Sin⁻¹ ( 1/ (2x² - 1))
=> Siny = 1/(2x² - 1)
=> Cosy dy/dx = ( -1/(2x² - 1)²)(4x)
=> Cosy dy/dx = -4x/(2x² - 1)²
Cosy =√( 1 - Sin²y)
= √( 1 - (1/(2x² - 1))²)
= 2x√(x² - 1) / (2x² - 1)
2x√(x² - 1) / (2x² - 1) dy/dx = -4x/(2x² - 1)²
=> dy/dx = - 2 / (2x² - 1)√(x² - 1)
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