UPSC NDA Math Model Paper 9

Given, √x+√y=2
√x=2−√y .... (1)
or √y=2−√x
Taking derivative on both sides, we get
⇒

1

2√y

dy

dx

=0−

1

2√x

⇒

dy

dx

=−

√y

√x

From equation (1), we have
⇒

dy

dx

=−

√y

2−√y

To find

dy

dx

at y=1, put y=1 in above equation.
⇒

dy

dx

=−

√1

2−√1

⇒

dy

dx

=−1
Hence, If
√x+√y=2, then

dy

dx

at y=1 equal to −1