Question

differentiate x^y=e^x-y​

Answer 1

Step-by-step explanation:

x

y

=e

x−y

Take log

e

on both sidees

log

e

x

y

=log

e

e

x−y

⇒ ylogx=(x−y)log

e

e

ylogx=x−y ⟶(1)

y[logx+1]=x

Differentiate both sides w.r.t. x

dx

dy

[1+logx]+y[

x

1

]=1

dx

dy

=

1+logx

1−

x

y

From eqn.(1)

x

y

=

(1+logx)

1

dx

dy

=

1+logx

1−

1+logx

1

=

(1+logx)

2

logx