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Exam: Maharashtra HSC Class 12
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Set · 10 questions
Differentiate the following w.r.t.
x
x
x
Q526
#526
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
e
3
sin
2
x
−
2
cos
2
x
e^{3\sin^2 x - 2\cos^2 x}
e
3
s
i
n
2
x
−
2
c
o
s
2
x
Show model answer
[QEx 1.1 Q.2 (ix) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q527
#527
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
cos
2
[
log
(
x
2
+
7
)
]
\cos^2\left[\log\left(x^2 + 7\right)\right]
cos
2
[
lo
g
(
x
2
+
7
)
]
Show model answer
[QEx 1.1 Q.2 (x) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q528
#528
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
tan
[
cos
(
sin
x
)
]
\tan\left[\cos\left(\sin x\right)\right]
tan
[
cos
(
sin
x
)
]
Show model answer
[QEx 1.1 Q.2 (xi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q529
#529
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
sec
[
tan
(
x
4
+
4
)
]
\sec\left[\tan\left(x^4 + 4\right)\right]
sec
[
tan
(
x
4
+
4
)
]
Show model answer
[QEx 1.1 Q.2 (xii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q530
#530
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Hard
Add
e
log
[
(
log
x
)
2
−
log
x
2
]
e^{\log\left[(\log x)^2 - \log x^2\right]}
e
l
o
g
[
(
l
o
g
x
)
2
−
l
o
g
x
2
]
Show model answer
[QEx 1.1 Q.2 (xiii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q531
#531
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Hard
Add
sin
sin
x
\sin \sqrt{\sin \sqrt{x}}
sin
sin
x
Show model answer
[QEx 1.1 Q.2 (xiv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q532
#532
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
log
[
sec
(
e
x
2
)
]
\log\left[\sec\left(e^{x^2}\right)\right]
lo
g
[
sec
(
e
x
2
)
]
Show model answer
[QEx 1.1 Q.2 (xv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q533
#533
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
log
e
2
(
log
x
)
\log_{e^2}\left(\log x\right)
lo
g
e
2
(
lo
g
x
)
Show model answer
[QEx 1.1 Q.2 (xvi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q534
#534
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
[
log
[
log
(
log
x
)
]
]
2
\left[\log\left[\log(\log x)\right]\right]^2
[
lo
g
[
lo
g
(
lo
g
x
)
]
]
2
Show model answer
[QEx 1.1 Q.2 (xvii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q535
#535
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
sin
2
x
2
−
cos
2
x
2
\sin^2 x^2 - \cos^2 x^2
sin
2
x
2
−
cos
2
x
2
Show model answer
[QEx 1.1 Q.2 (xviii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 15 questions
Differentiate the following w.r.t.
x
x
x
Q536
#536
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Easy
Add
(
x
2
+
4
x
+
1
)
3
+
(
x
3
−
5
x
−
2
)
4
\left(x^2 + 4x + 1\right)^3 + \left(x^3 - 5x - 2\right)^4
(
x
2
+
4
x
+
1
)
3
+
(
x
3
−
5
x
−
2
)
4
Show model answer
[QEx 1.1 Q.3 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q537
#537
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
(
1
+
4
x
)
5
(
3
+
x
−
x
2
)
8
\left(1 + 4x\right)^5 \left(3 + x - x^2\right)^8
(
1
+
4
x
)
5
(
3
+
x
−
x
2
)
8
Show model answer
[QEx 1.1 Q.3 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q538
#538
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
x
7
−
3
x
\frac{x}{\sqrt{7 - 3x}}
7
−
3
x
x
Show model answer
[QEx 1.1 Q.3 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q539
#539
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
(
x
3
−
5
)
5
(
x
3
+
3
)
3
\frac{\left(x^3 - 5\right)^5}{\left(x^3 + 3\right)^3}
(
x
3
+
3
)
3
(
x
3
−
5
)
5
Show model answer
[QEx 1.1 Q.3 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q540
#540
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
(
1
+
sin
2
x
)
2
(
1
+
cos
2
x
)
3
\left(1 + \sin^2 x\right)^2 \left(1 + \cos^2 x\right)^3
(
1
+
sin
2
x
)
2
(
1
+
cos
2
x
)
3
Show model answer
[QEx 1.1 Q.3 (v) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q541
#541
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
cos
x
+
cos
x
\sqrt{\cos x} + \sqrt{\cos \sqrt{x}}
cos
x
+
cos
x
Show model answer
[QEx 1.1 Q.3 (vi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q542
#542
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
log
(
sec
3
x
+
tan
3
x
)
\log\left(\sec 3x + \tan 3x\right)
lo
g
(
sec
3
x
+
tan
3
x
)
Show model answer
[QEx 1.1 Q.3 (vii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q543
#543
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
1
+
sin
x
∘
1
−
sin
x
∘
\frac{1 + \sin x^\circ}{1 - \sin x^\circ}
1
−
s
i
n
x
∘
1
+
s
i
n
x
∘
Show model answer
[QEx 1.1 Q.3 (viii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q544
#544
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
cot
(
log
x
2
)
−
log
(
cot
x
2
)
\cot\left(\frac{\log x}{2}\right) - \log\left(\frac{\cot x}{2}\right)
cot
(
2
l
o
g
x
)
−
lo
g
(
2
c
o
t
x
)
Show model answer
[QEx 1.1 Q.3 (ix) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q545
#545
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
e
2
x
−
e
−
2
x
e
2
x
+
e
−
2
x
\frac{e^{2x} - e^{-2x}}{e^{2x} + e^{-2x}}
e
2
x
+
e
−
2
x
e
2
x
−
e
−
2
x
Show model answer
[QEx 1.1 Q.3 (x) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q546
#546
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
e
x
+
1
e
x
−
1
\frac{e^{\sqrt{x}} + 1}{e^{\sqrt{x}} - 1}
e
x
−
1
e
x
+
1
Show model answer
[QEx 1.1 Q.3 (xi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q547
#547
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Moderate
Add
log
[
tan
3
x
⋅
sin
4
x
⋅
(
x
2
+
7
)
7
]
\log\left[\tan^3 x \cdot \sin^4 x \cdot \left(x^2 + 7\right)^7\right]
lo
g
[
tan
3
x
⋅
sin
4
x
⋅
(
x
2
+
7
)
7
]
Show model answer
[QEx 1.1 Q.3 (xii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q548
#548
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Hard
Add
log
(
1
−
cos
3
x
1
+
cos
3
x
)
\log\left(\sqrt{\frac{1 - \cos 3x}{1 + \cos 3x}}\right)
lo
g
(
1
+
c
o
s
3
x
1
−
c
o
s
3
x
)
Show model answer
[QEx 1.1 Q.3 (xiii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q549
#549
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Hard
Add
log
(
1
+
cos
(
5
x
2
)
1
−
cos
(
5
x
2
)
)
\log\left(\sqrt{\frac{1 + \cos\left(\frac{5x}{2}\right)}{1 - \cos\left(\frac{5x}{2}\right)}}\right)
lo
g
(
1
−
c
o
s
(
2
5
x
)
1
+
c
o
s
(
2
5
x
)
)
Show model answer
[QEx 1.1 Q.3 (xiv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Q550
#550
Mathematics → Differentiation → Derivatives of Composite Functions (Chain Rule)
·
Hard
Add
log
(
1
−
sin
x
1
+
sin
x
)
\log\left(\sqrt{\frac{1 - \sin x}{1 + \sin x}}\right)
lo
g
(
1
+
s
i
n
x
1
−
s
i
n
x
)
Show model answer
[QEx 1.1 Q.3 (xv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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