Question

Differentiate the function w.r.t.x:
(1 - 2 tan x)(5 + 4 sin x)

Answer 1

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Answer 2

We know that

$\frac{d {x}^{n} }{dx} = n {x}^{n - 1} \\ \\ \frac{d \: sin\: x}{dx} = cos\: x \\ \\\frac{d \: tan\: x}{dx} = sec^{2}\: x$
So, to differentiate given function with respect to x, we have to apply UV formula of differentiation.

$\frac{d(UV)}{dx} = U \frac{dV}{dx} + V\frac{dU}{dx} \\ \\ here \: U = (1-2\:tan\:x) \\ \\ V = (5+4sin \: x) \\ \\ \frac{d[(1-2\:tan\:x) \: (5+4sin \: x)]}{dx} =\\\\ (1-2\:tan\:x) \bigg(\frac{d \: (5+4sin \: x)}{dx}\bigg) + (5+4sin \: x)\bigg(\frac{d (1-2\:tan\:x) }{dx}\bigg) \\ \\\frac{d[(1-2\:tan\:x) \: (5+4sin \: x)]}{dx}\\\\ = (1-2\:tan\:x)[0+4 cos\: x]+(5+4sin \: x)(0-2sec^{2}\: x) \\ \\= (1-2\:tan\:x)[4 cos\: x]-2(5+4sin \: x)(sec^{2}\: x)$
Hope it helps you.