Business Studies, asked by parii61, 28 days ago

Find the derivative of f(x)=tan(x/x+1) by first principle.​

Answers

Answered by meghakharbikar05
1

Explanation:

From the first 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

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