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Exam: Maharashtra HSC Class 12
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Set · 1 question
Differentiate the following w. r. t. x.
Q576
#576
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
sin
2
(
sin
−
1
(
x
2
)
)
\sin^2\left(\sin^{-1}(x^2)\right)
sin
2
(
sin
−
1
(
x
2
)
)
Show model answer
[Q1.2.6 SolvedEx.2 (vi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 5 questions
Differentiate the following w. r. t. x.
Q577
#577
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
cos
−
1
(
4
cos
3
x
−
3
cos
x
)
\cos^{-1}(4\cos^3 x-3\cos x)
cos
−
1
(
4
cos
3
x
−
3
cos
x
)
Show model answer
[Q1.2.6 SolvedEx.3 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q578
#578
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
cos
−
1
[
sin
(
4
x
)
]
\cos^{-1}\left[\sin(4^x)\right]
cos
−
1
[
sin
(
4
x
)
]
Show model answer
[Q1.2.6 SolvedEx.3 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q579
#579
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
sin
−
1
(
1
−
cos
x
2
)
\sin^{-1}\left(\sqrt{\frac{1-\cos x}{2}}\right)
sin
−
1
(
2
1
−
c
o
s
x
)
Show model answer
[Q1.2.6 SolvedEx.3 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q580
#580
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
tan
−
1
(
1
−
cos
3
x
sin
3
x
)
\tan^{-1}\left(\frac{1-\cos 3x}{\sin 3x}\right)
tan
−
1
(
s
i
n
3
x
1
−
c
o
s
3
x
)
Show model answer
[Q1.2.6 SolvedEx.3 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q581
#581
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
cot
−
1
(
cos
x
1
+
sin
x
)
\cot^{-1}\left(\frac{\cos x}{1+\sin x}\right)
cot
−
1
(
1
+
s
i
n
x
c
o
s
x
)
Show model answer
[Q1.2.6 SolvedEx.3 (v) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 3 questions
Differentiate the following w. r. t. x.
Q582
#582
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
sin
−
1
(
2
cos
x
+
3
sin
x
13
)
\sin^{-1}\left(\frac{2\cos x+3\sin x}{\sqrt{13}}\right)
sin
−
1
(
13
2
c
o
s
x
+
3
s
i
n
x
)
Show model answer
[Q1.2.6 SolvedEx.4 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q583
#583
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
cos
−
1
(
3
sin
x
2
+
4
cos
x
2
5
)
\cos^{-1}\left(\frac{3\sin x^2+4\cos x^2}{5}\right)
cos
−
1
(
5
3
s
i
n
x
2
+
4
c
o
s
x
2
)
Show model answer
[Q1.2.6 SolvedEx.4 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q584
#584
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
sin
−
1
(
a
cos
x
−
b
sin
x
a
2
+
b
2
)
\sin^{-1}\left(\frac{a\cos x-b\sin x}{\sqrt{a^2+b^2}}\right)
sin
−
1
(
a
2
+
b
2
a
c
o
s
x
−
b
s
i
n
x
)
Show model answer
[Q1.2.6 SolvedEx.4 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 9 questions
Differentiate the following w. r. t. x.
Q585
#585
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
sin
−
1
(
2
x
1
+
x
2
)
\sin^{-1}\left(\frac{2x}{1+x^2}\right)
sin
−
1
(
1
+
x
2
2
x
)
Show model answer
[Q1.2.6 SolvedEx.5 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q586
#586
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
cos
−
1
(
2
x
1
−
x
2
)
\cos^{-1}\left(2x\sqrt{1-x^2}\right)
cos
−
1
(
2
x
1
−
x
2
)
Show model answer
[Q1.2.6 SolvedEx.5 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q587
#587
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
cosec
−
1
(
1
3
x
−
4
x
3
)
\operatorname{cosec}^{-1}\left(\frac{1}{3x-4x^3}\right)
cosec
−
1
(
3
x
−
4
x
3
1
)
Show model answer
[Q1.2.6 SolvedEx.5 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q588
#588
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
tan
−
1
(
2
e
x
1
−
e
2
x
)
\tan^{-1}\left(\frac{2e^x}{1-e^{2x}}\right)
tan
−
1
(
1
−
e
2
x
2
e
x
)
Show model answer
[Q1.2.6 SolvedEx.5 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q589
#589
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
cos
−
1
(
1
−
9
x
2
1
+
9
x
2
)
\cos^{-1}\left(\frac{1-9x^2}{1+9x^2}\right)
cos
−
1
(
1
+
9
x
2
1
−
9
x
2
)
Show model answer
[Q1.2.6 SolvedEx.5 (v) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q590
#590
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
cos
−
1
(
2
x
−
2
−
x
2
x
+
2
−
x
)
\cos^{-1}\left(\frac{2^x-2^{-x}}{2^x+2^{-x}}\right)
cos
−
1
(
2
x
+
2
−
x
2
x
−
2
−
x
)
Show model answer
[Q1.2.6 SolvedEx.5 (vi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q591
#591
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
tan
−
1
(
3
−
x
3
+
x
)
\tan^{-1}\left(\sqrt{\frac{3-x}{3+x}}\right)
tan
−
1
(
3
+
x
3
−
x
)
Show model answer
[Q1.2.6 SolvedEx.5 (vii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q592
#592
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
sin
−
1
(
5
1
−
x
2
−
12
x
13
)
\sin^{-1}\left(\frac{5\sqrt{1-x^2}-12x}{13}\right)
sin
−
1
(
13
5
1
−
x
2
−
12
x
)
Show model answer
[Q1.2.6 SolvedEx.5 (viii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q593
#593
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
sin
−
1
(
2
x
+
1
1
+
4
x
)
\sin^{-1}\left(\frac{2^{x+1}}{1+4^x}\right)
sin
−
1
(
1
+
4
x
2
x
+
1
)
Show model answer
[Q1.2.6 SolvedEx.5 (ix) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Set · 4 questions
Differentiate the following w. r. t. x.
Q594
#594
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
tan
−
1
(
4
x
1
+
21
x
2
)
\tan^{-1}\left(\frac{4x}{1+21x^2}\right)
tan
−
1
(
1
+
21
x
2
4
x
)
Show model answer
[Q1.2.6 SolvedEx.6 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q595
#595
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
tan
−
1
(
7
x
1
−
12
x
2
)
\tan^{-1}\left(\frac{7x}{1-12x^2}\right)
tan
−
1
(
1
−
12
x
2
7
x
)
Show model answer
[Q1.2.6 SolvedEx.6 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q596
#596
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
cot
−
1
(
b
sin
x
−
a
cos
x
a
sin
x
+
b
cos
x
)
\cot^{-1}\left(\frac{b\sin x-a\cos x}{a\sin x+b\cos x}\right)
cot
−
1
(
a
s
i
n
x
+
b
c
o
s
x
b
s
i
n
x
−
a
c
o
s
x
)
Show model answer
[Q1.2.6 SolvedEx.6 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q597
#597
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
tan
−
1
(
5
x
+
1
3
−
x
−
6
x
2
)
\tan^{-1}\left(\frac{5x+1}{3-x-6x^2}\right)
tan
−
1
(
3
−
x
−
6
x
2
5
x
+
1
)
Show model answer
[Q1.2.6 SolvedEx.6 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Set · 3 questions
Find the derivative of the function
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
using the derivative of the inverse function
x
=
f
−
1
(
y
)
x=f^{-1}(y)
x
=
f
−
1
(
y
)
in the following
Q598
#598
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Easy
Add
y
=
x
y=\sqrt{x}
y
=
x
Show model answer
[QEx 1.2 Q.1 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q599
#599
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Moderate
Add
y
=
2
−
x
y=\sqrt{2-\sqrt{x}}
y
=
2
−
x
Show model answer
[QEx 1.2 Q.1 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q600
#600
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Easy
Add
y
=
x
−
2
3
y=\sqrt[3]{x-2}
y
=
3
x
−
2
Show model answer
[QEx 1.2 Q.1 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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