Question

Find Dy/DX if
Y=sin^-1(2x)

Answer 1

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