Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > For x > 1,(2x)2y = 4e2x − 2y, then (...
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For x > 1,(2x)
2y
= 4e
2x − 2y
, then (1 + log
e
2x)
2
dy/dx is equal to:
- a)
- b)loge2x
- c)
- d)x loge2x
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
For x > 1,(2x)2y = 4e2x − 2y, then (1 + loge2x)2dy/dx is equa...
Given,
(2x)
2y
= 4e
2x − 2y
log
b
(M
p
) = plog
b
(M)
log
b
(MN) = log
b
(M) + log
b
(N)
Taking log both sides, we get
ln (2x)
2y
= ln 4e
2x − 2y
⇒ ln (2x)
2y
= ln 4+ln (2x − 2y)
⇒ 2yln (2x) = ln 2
2
+ (2x−2y)
⇒ 2yln (2x) = 2ln 2+(2x−2y)… (1)
⇒ yln (2x) = ln 2+(x−y)
⇒ y(1+ln 2x) = x+ln 2
∴ y = x + ln 2/1 + ln (2x)…(2)
As we know,
d/dx(lnx) = 1/x
If f and g are both differentiable, then,
Differentiating equation (1) with respect to x, we get,
Putting equation (2) in equation (3), we get,
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For x > 1,(2x)2y = 4e2x − 2y, then (1 + loge2x)2dy/dx is equal to:a)b)loge2xc)d)x loge2xCorrect answer is option 'A'. Can you explain this answer?
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