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Question
If y = `25^(log_5sin_x) + 16^(log_4cos_x)` then `("d"y)/("d"x)` = ______.
Options
1
0
9
cos x – sin x
Solution
If y = `25^(log_5sin_x) + 16^(log_4cos_x)` then `("d"y)/("d"x)` 0.
Explanation:
`y = 25^(log_5 sinx) + 16^(log_4 cosx)`
`y = 5^(2 log_5 sinx) + 4^(2 log_4 cosx)`
`y = 5^(log_5 sin^2x) + 4^(log_4 cos^2x) ...[m log n = log n^3]`
y = sin2x + cos2x ...[alogax = x]
y = 1
then `dy/dx = 0`
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