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Question
Differentiate the following w.r.t.x:
y = (25)log5(secx) − (16)log4(tanx)
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Solution
y = (25)log5(secx) − (16)log4(tanx)
y = (52)log5(secx) − (42)log4(tanx)
y = (5)2log5(secx) − (4)2log4(tanx)
`y = (5)^(log_5 (sec^2x)) - (4)^(log_4(tan^2x))`
y = sec2x – tan2x ...`[ ∵ a^(log_ax) = x]`
∴ y = 1
Differentiating w.r.t.x, we get,
`"dy"/"dx" = "d"/"dx"(1)`
`"dy"/"dx"` = 0.
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