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Exam: Maharashtra HSC Class 12
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Set · 5 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
Q601
#601
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Easy
Add
y
=
log
(
2
x
−
1
)
y=\log(2x-1)
y
=
lo
g
(
2
x
−
1
)
Show model answer
[QEx 1.2 Q.1 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q602
#602
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Easy
Add
y
=
2
x
+
3
y=2x+3
y
=
2
x
+
3
Show model answer
[QEx 1.2 Q.1 (v) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q603
#603
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Easy
Add
y
=
e
x
−
3
y=e^x-3
y
=
e
x
−
3
Show model answer
[QEx 1.2 Q.1 (vi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q604
#604
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Easy
Add
y
=
e
2
x
−
3
y=e^{2x-3}
y
=
e
2
x
−
3
Show model answer
[QEx 1.2 Q.1 (vii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q605
#605
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Moderate
Add
y
=
log
2
(
x
2
)
y=\log_2\left(\frac{x}{2}\right)
y
=
lo
g
2
(
2
x
)
Show model answer
[QEx 1.2 Q.1 (viii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 5 questions
Find the derivative of the inverse function of the following
Q606
#606
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Moderate
Add
y
=
x
2
⋅
e
x
y=x^2\cdot e^x
y
=
x
2
⋅
e
x
Show model answer
[QEx 1.2 Q.2 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q607
#607
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Moderate
Add
y
=
x
cos
x
y=x\cos x
y
=
x
cos
x
Show model answer
[QEx 1.2 Q.2 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q608
#608
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Moderate
Add
y
=
x
⋅
7
x
y=x\cdot 7^x
y
=
x
⋅
7
x
Show model answer
[QEx 1.2 Q.2 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q609
#609
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Moderate
Add
y
=
x
2
+
log
x
y=x^2+\log x
y
=
x
2
+
lo
g
x
Show model answer
[QEx 1.2 Q.2 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q610
#610
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Moderate
Add
y
=
x
log
x
y=x\log x
y
=
x
lo
g
x
Show model answer
[QEx 1.2 Q.2 (v) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 4 questions
Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them.
Q611
#611
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Moderate
Add
y
=
x
5
+
2
x
3
+
3
x
y=x^5+2x^3+3x
y
=
x
5
+
2
x
3
+
3
x
, at
x
=
1
x=1
x
=
1
Show model answer
[QEx 1.2 Q.3 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q612
#612
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Moderate
Add
y
=
e
x
+
3
x
+
2
y=e^x+3x+2
y
=
e
x
+
3
x
+
2
, at
x
=
0
x=0
x
=
0
Show model answer
[QEx 1.2 Q.3 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q613
#613
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Moderate
Add
y
=
3
x
2
+
2
log
x
3
y=3x^2+2\log x^3
y
=
3
x
2
+
2
lo
g
x
3
, at
x
=
1
x=1
x
=
1
Show model answer
[QEx 1.2 Q.3 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q614
#614
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Moderate
Add
y
=
sin
(
x
−
2
)
+
x
2
y=\sin(x-2)+x^2
y
=
sin
(
x
−
2
)
+
x
2
, at
x
=
2
x=2
x
=
2
Show model answer
[QEx 1.2 Q.3 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q615
#615
Mathematics → Differentiation → Derivatives of Inverse Functions
·
Moderate
Add
If
f
(
x
)
=
x
3
+
x
−
2
f(x)=x^3+x-2
f
(
x
)
=
x
3
+
x
−
2
, find
(
f
−
1
)
′
(
0
)
(f^{-1})'(0)
(
f
−
1
)
′
(
0
)
.
Show model answer
[QEx 1.2 Q.4 · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 2 questions
Using derivative prove
Q616
#616
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
tan
−
1
x
+
cot
−
1
x
=
π
2
\tan^{-1}x+\cot^{-1}x=\frac{\pi}{2}
tan
−
1
x
+
cot
−
1
x
=
2
π
Show model answer
[QEx 1.2 Q.5 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q617
#617
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
sec
−
1
x
+
cosec
−
1
x
=
π
2
\sec^{-1}x+\operatorname{cosec}^{-1}x=\frac{\pi}{2}
sec
−
1
x
+
cosec
−
1
x
=
2
π
... [for
∣
x
∣
≥
1
|x|\geq 1
∣
x
∣
≥
1
]
Show model answer
[QEx 1.2 Q.5 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 8 questions
Differentiate the following w. r. t. x.
Q618
#618
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Easy
Add
tan
−
1
(
log
x
)
\tan^{-1}(\log x)
tan
−
1
(
lo
g
x
)
Show model answer
[QEx 1.2 Q.6 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q619
#619
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
cosec
−
1
(
e
−
x
)
\operatorname{cosec}^{-1}(e^{-x})
cosec
−
1
(
e
−
x
)
Show model answer
[QEx 1.2 Q.6 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q620
#620
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Easy
Add
cot
−
1
(
x
3
)
\cot^{-1}(x^3)
cot
−
1
(
x
3
)
Show model answer
[QEx 1.2 Q.6 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q621
#621
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Easy
Add
cot
−
1
(
4
x
)
\cot^{-1}(4^x)
cot
−
1
(
4
x
)
Show model answer
[QEx 1.2 Q.6 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q622
#622
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Easy
Add
tan
−
1
(
x
)
\tan^{-1}(\sqrt{x})
tan
−
1
(
x
)
Show model answer
[QEx 1.2 Q.6 (v) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q623
#623
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
sin
−
1
(
1
+
x
2
2
)
\sin^{-1}\left(\sqrt{\frac{1+x^2}{2}}\right)
sin
−
1
(
2
1
+
x
2
)
Show model answer
[QEx 1.2 Q.6 (vi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q624
#624
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
cos
−
1
(
1
−
x
2
)
\cos^{-1}(1-x^2)
cos
−
1
(
1
−
x
2
)
Show model answer
[QEx 1.2 Q.6 (vii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q625
#625
Mathematics → Differentiation → Derivatives of Inverse Trigonometric Functions
·
Moderate
Add
sin
−
1
(
x
3
2
)
\sin^{-1}\left(x^{\frac{3}{2}}\right)
sin
−
1
(
x
2
3
)
Show model answer
[QEx 1.2 Q.6 (viii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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