find the derivative of tan x from the first principle
Answers
Answered by
3
Answer:
Find the derivative of tan x using first principle of derivatives
ANSWER
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
Step-by-step explanation:
Hope you have satisfied with this answer.So please follow me and thank me and make me as brainlesset soon and vote my answer.
Similar questions