Tentukan turunan pertama fungsi trigonometri berikut! f(x) = cos x / tan x

Rani Maharani

Tentukan turunan pertama fungsi trigonometri berikut!

f(x) = cos x / tan x

Pembahasan

Langkah-langkahnya adalah sebagai berikut:

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Selanjutnya, kita dapat menghitung turunan pertama dari $f(x)$ menggunakan aturan pembagian dan aturan rantai seperti berikut:

f^{'} (x) = \frac{d}{d x} [\frac{cos ^{2} x}{sin x}] = \frac{sin x \cdot \frac{d}{d x} [ cos ^{2} x ] - cos ^{2} x \cdot \frac{d}{d x} [ sin x ]}{sin ^{2} x} = \frac{2 cos x \cdot ( - sin x ) - cos ^{2} x \cdot cos x}{sin ^{2} x} = \frac{- 2 cos ^{2} x + cos ^{3} x}{sin ^{2} x} = \frac{cos x ( - 2 cos x + cos ^{2} x )}{sin ^{2} x} = \frac{cos x ( 1 - 2 sin ^{2} x )}{sin ^{2} x} = \frac{cos x}{sin ^{2} x} - \frac{2 cos x sin ^{2} x}{sin ^{4} x} = csc x - 2 cot x

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