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Question

Differentiate the following functions with respect to x:
(12 tan x)(5+4 sin x)

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Solution

We have,
Differentiate the following functions with respect to x:
ddx{(12 tan x)(5+4 sin x)}
=(5+4 sin x)ddx(12 tan x)+(12 tan x)ddx(5+4 sin x) [Using product rule]
=(5+4 sin x)(02 sec2x)+(12 tan x)(0+4 cos x)
=10sec2x8 sinx×sec2x+4cosx8 cosx×tan x
=4(52sec2x2 sin x×1cos2x+cos x2 cos x×sin xcos x)
=4(52sec2x2 tanx sec x+cos x2 sin x)
=4(cos x2 sin x2 tanx secx52sec2x)

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