Question

By first principle of derivative log tanx

Answer 1

Answer... sec²x ans..

derivation t principle of derivatives,

f

′

(x)=

h→0

lim

h

f(x+h)−f(x)

=

h→0

lim

h

tan(x+h)−tanx

=

h→0

lim

h

cos(x+h)

sin(x+h)

−

cosx

sinx

=

h→0

lim

hcosxcos(x+h)

cosxsin(x+h)−sinxcos(x+h)

=

h→0

lim

hcosxcos(x+h)

2

sin(2x+h)+sinh

−

2

sin(2x+h)−sinh

=

h→0

lim

hcosxcos(x+h)

sinh

=

h→0

lim

h

sinh

×

h→0

lim

cosxcos(x+h)

1

=1×

cosx×cosx

1

=

cos

2

x

1

f

′

(x)=sec

2

x