Question

solve the above question​

Answer 1

Step-by-step explanation:

Given---> y = eˣ + e⁻ˣ

To find---> Value of

dy / dx - √(y² - 4 )

Solution--->

1) plzz refer the attachment

2) In second step we differentiate the given relation with respect to x by using formulee,

d / dx ( eˣ ) = eˣ

d / dx ( e⁻ˣ ) = - e⁻ˣ

3) then we put value of dy / dx and y in

( dy / dx ) - √(y² - 4 )

4) In 8th step we use an identity

( a + b )² = a² + b² + 2ab

5) Then in 14th step we use an identity

a² + b² - 2ab = ( a - b )²

Additional information--->

1) d / dx ( xⁿ ) = n xⁿ⁻¹

2) d / dx ( aˣ ) = aˣ loga

3) d / dx ( Sinx ) = Cosx

4) d / dx ( Cosx ) = - Sinx

5) d / dx ( tanx ) = Sec²x

6) d / dx ( Secx ) = Secx tanx

7) d / dx ( Cotx ) = - Cosec²x

8) d / dx ( Cosecx ) = - Cosecx Cotx

9) d / dx ( logx ) = 1 / x