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Exam: Maharashtra HSC Class 12
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Set · 7 questions
Differentiate the following w. r. t. x.
Q651
#651
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
cos
−
1
(
e
x
−
e
−
x
e
x
+
e
−
x
)
\cos^{-1}\left(\frac{e^x-e^{-x}}{e^x+e^{-x}}\right)
cos
−
1
(
e
x
+
e
−
x
e
x
−
e
−
x
)
Show model answer
[QEx 1.2 Q.9 (vi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q652
#652
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
cos
−
1
(
1
−
9
x
1
+
9
x
)
\cos^{-1}\left(\frac{1-9^x}{1+9^x}\right)
cos
−
1
(
1
+
9
x
1
−
9
x
)
Show model answer
[QEx 1.2 Q.9 (vii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q653
#653
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
sin
−
1
(
4
x
+
1
2
1
+
2
4
x
)
\sin^{-1}\left(\frac{4^{x+\frac{1}{2}}}{1+2^{4x}}\right)
sin
−
1
(
1
+
2
4
x
4
x
+
2
1
)
Show model answer
[QEx 1.2 Q.9 (viii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q654
#654
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
sin
−
1
(
1
−
25
x
2
1
+
25
x
2
)
\sin^{-1}\left(\frac{1-25x^2}{1+25x^2}\right)
sin
−
1
(
1
+
25
x
2
1
−
25
x
2
)
Show model answer
[QEx 1.2 Q.9 (ix) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q655
#655
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
sin
−
1
(
1
−
x
3
1
+
x
3
)
\sin^{-1}\left(\frac{1-x^3}{1+x^3}\right)
sin
−
1
(
1
+
x
3
1
−
x
3
)
Show model answer
[QEx 1.2 Q.9 (x) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q656
#656
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
tan
−
1
(
2
x
5
2
1
−
x
5
)
\tan^{-1}\left(\frac{2x^{\frac{5}{2}}}{1-x^5}\right)
tan
−
1
(
1
−
x
5
2
x
2
5
)
Show model answer
[QEx 1.2 Q.9 (xi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q657
#657
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
cot
−
1
(
1
−
x
1
+
x
)
\cot^{-1}\left(\frac{1-\sqrt{x}}{1+\sqrt{x}}\right)
cot
−
1
(
1
+
x
1
−
x
)
Show model answer
[QEx 1.2 Q.9 (xii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 9 questions
Differentiate the following w. r. t. x.
Q658
#658
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
tan
−
1
(
8
x
1
−
15
x
2
)
\tan^{-1}\left(\frac{8x}{1-15x^2}\right)
tan
−
1
(
1
−
15
x
2
8
x
)
Show model answer
[QEx 1.2 Q.10 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q659
#659
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
cot
−
1
(
1
+
35
x
2
2
x
)
\cot^{-1}\left(\frac{1+35x^2}{2x}\right)
cot
−
1
(
2
x
1
+
35
x
2
)
Show model answer
[QEx 1.2 Q.10 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q660
#660
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
tan
−
1
(
2
x
1
+
3
x
)
\tan^{-1}\left(\frac{2\sqrt{x}}{1+3x}\right)
tan
−
1
(
1
+
3
x
2
x
)
Show model answer
[QEx 1.2 Q.10 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q661
#661
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
tan
−
1
(
2
x
+
2
1
−
3
(
4
x
)
)
\tan^{-1}\left(\frac{2^{x+2}}{1-3(4^x)}\right)
tan
−
1
(
1
−
3
(
4
x
)
2
x
+
2
)
Show model answer
[QEx 1.2 Q.10 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q662
#662
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
tan
−
1
(
2
x
1
+
2
2
x
+
1
)
\tan^{-1}\left(\frac{2^x}{1+2^{2x+1}}\right)
tan
−
1
(
1
+
2
2
x
+
1
2
x
)
Show model answer
[QEx 1.2 Q.10 (v) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q663
#663
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
cot
−
1
(
a
2
−
6
x
2
5
a
x
)
\cot^{-1}\left(\frac{a^2-6x^2}{5ax}\right)
cot
−
1
(
5
a
x
a
2
−
6
x
2
)
Show model answer
[QEx 1.2 Q.10 (vi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q664
#664
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
tan
−
1
(
a
+
b
tan
x
b
−
a
tan
x
)
\tan^{-1}\left(\frac{a+b\tan x}{b-a\tan x}\right)
tan
−
1
(
b
−
a
t
a
n
x
a
+
b
t
a
n
x
)
Show model answer
[QEx 1.2 Q.10 (vii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q665
#665
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
tan
−
1
(
5
−
x
6
x
2
−
5
x
−
3
)
\tan^{-1}\left(\frac{5-x}{6x^2-5x-3}\right)
tan
−
1
(
6
x
2
−
5
x
−
3
5
−
x
)
Show model answer
[QEx 1.2 Q.10 (viii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q666
#666
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Hard
Add
cot
−
1
(
4
−
x
−
2
x
2
3
x
+
2
)
\cot^{-1}\left(\frac{4-x-2x^2}{3x+2}\right)
cot
−
1
(
3
x
+
2
4
−
x
−
2
x
2
)
Show model answer
[QEx 1.2 Q.10 (ix) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 5 questions
Differentiate the following w. r. t. x.
Q667
#667
Mathematics → Differentiation → Logarithmic Differentiation
·
Moderate
Add
(
(
x
2
+
3
)
2
(
x
3
+
5
)
2
3
(
2
x
2
+
1
)
3
)
\left(\frac{(x^2+3)^2\ \sqrt[3]{(x^3+5)^2}}{\sqrt{(2x^2+1)^3}}\right)
(
(
2
x
2
+
1
)
3
(
x
2
+
3
)
2
3
(
x
3
+
5
)
2
)
Show model answer
[Q1.3.1 SolvedEx.1 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q668
#668
Mathematics → Differentiation → Logarithmic Differentiation
·
Hard
Add
e
x
2
(
tan
x
)
x
2
(
1
+
x
2
)
3
2
cos
3
x
\frac{e^{x^2}\ (\tan x)^{\frac{x}{2}}}{(1+x^2)^{\frac{3}{2}}\ \cos^3 x}
(
1
+
x
2
)
2
3
c
o
s
3
x
e
x
2
(
t
a
n
x
)
2
x
Show model answer
[Q1.3.1 SolvedEx.1 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q669
#669
Mathematics → Differentiation → Logarithmic Differentiation
·
Moderate
Add
(
x
+
1
)
3
2
(
2
x
+
3
)
5
2
(
3
x
+
4
)
2
3
(x+1)^{\frac{3}{2}}\ (2x+3)^{\frac{5}{2}}\ (3x+4)^{\frac{2}{3}}
(
x
+
1
)
2
3
(
2
x
+
3
)
2
5
(
3
x
+
4
)
3
2
Show model answer
[Q1.3.1 SolvedEx.1 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q670
#670
Mathematics → Differentiation → Logarithmic Differentiation
·
Moderate
Add
x
a
+
x
x
+
a
x
x^a + x^x + a^x
x
a
+
x
x
+
a
x
Show model answer
[Q1.3.1 SolvedEx.1 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q671
#671
Mathematics → Differentiation → Logarithmic Differentiation
·
Hard
Add
(
sin
x
)
tan
x
−
x
log
x
(\sin x)^{\tan x} - x^{\log x}
(
sin
x
)
t
a
n
x
−
x
l
o
g
x
Show model answer
[Q1.3.1 SolvedEx.1 (v) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 3 questions
Find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
if
Q672
#672
Mathematics → Differentiation → Derivatives of Implicit Functions
·
Easy
Add
x
5
+
x
y
3
+
x
2
y
+
y
4
=
4
x^5 + xy^3 + x^2y + y^4 = 4
x
5
+
x
y
3
+
x
2
y
+
y
4
=
4
Show model answer
[Q1.3.3 SolvedEx.1 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q673
#673
Mathematics → Differentiation → Derivatives of Implicit Functions
·
Moderate
Add
y
3
+
cos
(
x
y
)
=
x
2
−
sin
(
x
+
y
)
y^3 + \cos(xy) = x^2 - \sin(x + y)
y
3
+
cos
(
x
y
)
=
x
2
−
sin
(
x
+
y
)
Show model answer
[Q1.3.3 SolvedEx.1 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q674
#674
Mathematics → Differentiation → Derivatives of Implicit Functions
·
Moderate
Add
x
2
+
e
x
y
=
y
2
+
log
(
x
+
y
)
x^2 + e^{xy} = y^2 + \log(x + y)
x
2
+
e
x
y
=
y
2
+
lo
g
(
x
+
y
)
Show model answer
[Q1.3.3 SolvedEx.1 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q675
#675
Mathematics → Differentiation → Derivatives of Implicit Functions
·
Moderate
Add
Find
x
m
⋅
y
n
=
(
x
+
y
)
m
+
n
x^m \cdot y^n = (x + y)^{m + n}
x
m
⋅
y
n
=
(
x
+
y
)
m
+
n
, then prove that
d
y
d
x
=
y
x
\frac{dy}{dx} = \frac{y}{x}
d
x
d
y
=
x
y
.
Show model answer
[Q1.3.3 SolvedEx.2 · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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