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Find Dy/DX ifY=sin^-1(2x) |
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Answer» Answer: 2 / √( 1 - 4x² ) Step-by-step explanation: To find -----> DERIVATIVE of Sin⁻¹ ( 2x ) Solution------> We know that, 1) d/dx ( Sin⁻¹x ) = 1 / √1 - x² 2) d/dx ( x ) = 1 ATQ, y = Sin⁻¹ ( 2x ) Differentiating with respect to x , => dy/dx = d/dx ( Sin⁻¹ 2x ) = [ 1 / √{ 1 - ( 2x )² ] d/dx ( 2x ) = 1 / √( 1 - 4x² ) ( 2 × 1 ) = 2 / √( 1 - 4x² ) Additional information-----> 1) d/dx ( xⁿ ) = n xⁿ⁻¹ 2) d/dx ( eˣ ) = eˣ 3) d/dx ( aˣ ) = aˣ loga 4) d/dx ( logx ) = 1 / x 5) d/dx ( Sinx ) = Cosx 6) d/dx ( Cosx ) = - Sinx 7) d/dx ( tanx ) = Sec²x 8) d/dx ( Secx ) = Secx tanx 9) d/dx ( Cotx ) = - Cosec²x 10) d/dx ( Cosecx ) = - Cosecx Cotx |
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