Question

Find dy/dx of tan1/x

Answer 1

y

=

arctan

x

 

tan

y

=

x

sec

2

y

d

y

d

x

=

1

d

y

d

x

=

1

sec

2

y

Since  

tan

y

=

x

1

and  

√

1

2

+

x

2

=

√

1

+

x

2

,  

sec

2

y

=

(

√

1

+

x

2

1

)

2

=

1

+

x

2

⇒

d

y

d

x

=

1

1

+

x

2

I think he originally intended to do this:

d

y

d

x

=

1

sec

2

y

sec

2

y

=

1

+

tan

2

y

tan

2

y

=

x

→

sec

2

y

=

1

+

x

2

⇒

d

y

d

x

=

1

1

+

x

2

Answer 2

Answer:

we can't understand questoon