154
You visited us
154
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Integration of Trigonometric Functions
Differentiate...
Question
Differentiate the following functions from first principles:
sin
−1
(2
x
+ 3)
Open in App
Solution
Let
f
x
=
sin
-
1
2
x
+
3
⇒
f
x
+
h
=
sin
-
1
2
x
+
h
+
3
⇒
f
x
+
h
=
sin
-
1
2
x
+
2
h
+
3
∴
d
d
x
f
x
=
lim
h
→
0
f
x
+
h
-
f
x
h
=
lim
h
→
0
sin
-
1
2
x
+
2
h
+
3
-
sin
-
1
2
x
+
3
h
=
lim
h
→
0
sin
-
1
2
x
+
2
h
+
3
1
-
2
x
+
3
2
-
2
x
+
3
1
-
2
x
+
2
h
+
3
2
h
∵
sin
-
1
x
-
sin
-
1
y
=
sin
-
1
x
1
-
y
2
-
y
1
-
x
2
=
lim
h
→
0
sin
-
1
z
z
×
z
h
where
,
z
=
2
x
+
2
h
+
3
1
-
2
x
+
3
2
-
2
x
+
3
1
-
2
x
+
2
h
+
3
2
and
lim
h
→
0
sin
-
1
h
h
=
1
=
lim
h
→
0
z
h
=
lim
h
→
0
2
x
+
2
h
+
3
1
-
2
x
+
3
2
-
2
x
+
3
1
-
2
x
+
2
h
+
3
2
h
=
lim
h
→
0
2
x
+
2
h
+
3
2
1
-
2
x
+
3
2
-
2
x
+
3
2
1
-
2
x
+
2
h
+
3
2
h
2
x
+
2
h
+
3
1
-
2
x
+
3
2
+
2
x
+
3
1
-
2
x
+
2
h
+
3
2
Rationalizing
numerator
=
lim
h
→
0
2
x
+
3
2
+
4
h
2
+
4
h
2
x
+
3
1
-
2
x
+
3
2
-
2
x
+
3
2
1
-
2
x
+
3
2
-
4
h
2
-
4
h
2
x
+
3
h
2
x
+
2
h
+
3
1
-
2
x
+
3
2
+
2
x
+
3
1
-
2
x
+
2
h
+
3
2
=
lim
h
→
0
2
x
+
3
2
+
4
h
2
+
4
h
2
x
+
3
-
2
x
+
3
4
-
4
h
2
2
x
+
3
2
-
4
h
2
x
+
3
3
-
2
x
+
3
2
+
2
x
+
3
4
+
4
h
2
2
x
+
3
2
+
4
h
2
x
+
3
3
h
2
x
+
2
h
+
3
1
-
2
x
+
3
2
+
2
x
+
3
1
-
2
x
+
2
h
+
3
2
=
lim
h
→
0
4
h
h
+
2
x
+
3
h
2
x
+
2
h
+
3
1
-
2
x
+
3
2
+
2
x
+
3
1
-
2
x
+
2
h
+
3
2
=
4
2
x
+
3
2
x
+
3
1
-
2
x
+
3
2
+
2
x
+
3
1
-
2
x
+
3
2
=
4
2
x
+
3
2
2
x
+
3
1
-
2
x
+
3
2
=
2
1
-
2
x
+
3
2
∴
d
d
x
sin
-
1
2
x
+
3
=
2
1
-
2
x
+
3
2
Suggest Corrections
0
Similar questions
Q.
Differentiate the following functions from first principles:
(i)
e
cot
x
(ii) x
2
e
x
(iii) log cosec x
(iv) sin
−1
(2x + 3)
Q.
Differentiate the following functions from first principles:
e
3x
Q.
Differentiate the following functions w.r.t
x
(
i
)
cos
−
1
(
2
x
1
+
x
2
)
(
i
i
)
sin
−
1
(
2
x
√
1
−
x
2
)
Q.
Differentiate the following functions from first principles:
x
2
e
x
Q.
Differentiate the following functions from first principles:
log cosec
x
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Integration of Trigonometric Functions
MATHEMATICS
Watch in App
Explore more
Integration of Trigonometric Functions
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app
