Differentiation Test

Result

Differentiation Test - 6

Score
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Rank
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Weekly Quiz Competition

Question 1
4 / -1

If y = cos^–1 (cos x), the dy/dx is

A
1 in the whole plane

B
–1 in the whole plane

C
1 in the 2nd and 3 rd quadrants of the plane

D
–1 in the 3rd and 4th quadrants of the plane

Solution
Question 2
4 / -1

A

B

C

D

Solution
Question 3
4 / -1

A
0

B
tan t

C
1

D
sin t cos t

Solution
Question 4
4 / -1

If x^y = e^{x – y}, x > 0, then the value of dy/dx at (1, 1) is

A
0

B
1/2

C
1

D
2

Solution
Question 5
4 / -1

The value of differentiation of e^x² with respect to e^2x–1 at x = 1 is

A
e

B
0

C
e^–1

D
1

Solution
Question 6
4 / -1

A
0

B
1

C
π/4

D
√π

Solution
Question 7
4 / -1

A

B

C

D

Solution
Question 8
4 / -1

The derivative of f(tan x) with respect to g (sec x) at x = π/4, where f '(1) = 2 and g'(√2) = 4, is

A
1/√2

B
√2

C
1

D
None of these

Solution
Question 9
4 / -1

If y = xⁿ log x + x(log x)ⁿ, then dy/dx is equal to

A
x^{n –1} (1 + n log x) + (log x)^{n – 1} (n + log x)

B
x^{n – 2}(1 + n logx) + (log x)^{n – 1}(n + log x)

C
x^{n – 1}(1 + n log x) + (log x)^{n – 1} (n – log x)

D
None of these

Solution
Question 10
4 / -1

A
1

B
–1

C
2

D
0

Solution