Question

Plzz ans differentiation​

Answer 1

Answer:

HOPE IT HELPS YOU

MAKE IT BRAINLY ANSWER PLS

THANKS MY ALL ANSWERS PLS

@@@@@$$$$$$$@@@$@$@$@@@

Answer 2

Answer:

x^y - x ( x^y - x - 1 ) / ( x ) ( 1 - ( x^y - x ) .  ㏑ x )

Step-by-step explanation:

Given :

x + y = x^y

Rewrite as :

= > y = x^y - x

Taking ㏑ both side we get :

= > ㏑ y = ㏑ x^y - ㏑ x

= > ㏑ y = y . ㏑ x - ㏑ x

Diff. w.r.t. x we get :

= > 1 / y ( d y / d x ) = y (  ㏑ x )' +  ㏑ x ( y )' -  ㏑ x

= > 1 / y ( d y / d x ) =  y / x + y'  ㏑ x - 1 / x

= > 1 / y ( y )' - y' ㏑ x = ( y - 1 ) / x

= > y' ( 1 / y -  ㏑ x ) = ( y - 1 ) / x

= > y' ( 1 - y . ㏑ x ) = y ( y - 1 ) / x

= > y' = y ( y - 1 ) / ( x ) ( 1 - y .  ㏑ x )

Putting value of y = x^y - x

= > d y / d x = x^y - x ( x^y - x - 1 ) / ( x ) ( 1 - ( x^y - x ) .  ㏑ x )

Hence we get required answer!