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Question
9. log (log x)
Solution :
Let log (log x)
Question
10. sin(log x)
Solution :
Let sin (log x)
Question
11. If y = 5 cos x - 3 sin x pro
ve that
Solution :
Let y = 5 cos x - 3 sin x
Question
12. If y = cos
-1
x Find
Question
13. If y = 3 cos (log x) + 4 sin (log x), show that x
2
y
2
+ xy
1
+ y = 0
Solution :
Given: y = 3 cos (log x) + 4 sin (log x)
Hence proved.
Question
14. If y = Ae
mx
+ Be
nx
show that
Solution :
Given: y = Ae
mx
+ Be
nx
Hence proved.
Question
15. If 500e
7x
+ 600e
-7x
show that
Solution :
Given: 500e
7x
+ 600e
-7x
Hence proved.
Question
16. If e
y
(x + 1) = 1, show that
Solution :
Given: e
y
(x + 1) = 1
Taking log on both sides,
Differentiating this relationship with respect to
x
, we obtain
Hence proved.
Question
17. If y = (tan
-1
x)
2
show that
(x
2
+ 1)
2
y
2
+ 2(x
2
+ 1)y
1
= 2
Solution :
Given: y = (tan
-1
x)
2
Hence proved.
