Tentukan turunan pertama fungsi berikut f(x)= sec x - √8csc x

<p>Saya bantu jawab ya!</p><p>Untuk menjawab soal tersebut anda perlu memahami tentang aturan-aturan turunan, seperti :</p><p><strong>y = u/v, maka y' = (u'v - uv')/v²</strong></p><p>&nbsp;</p><p><strong>Sekarang kita tentukan dahulu :</strong></p><p><strong>y = sec(x)</strong></p><p><strong>y = 1/cos(x)</strong></p><p><strong>u = 1</strong></p><p><strong>u' = 0</strong></p><p><strong>v = cos(x)</strong></p><p><strong>v' = -sin(x)</strong></p><p>&nbsp;</p><p><strong>Jadi turunan y = sec(x) :</strong></p><p><strong>y' = (0 × cos(x) - (1)(-sin(x))/(cos(x))²</strong></p><p><strong>y' = sin(x)/cos²(x)</strong></p><p><strong>y' = sin(x)/cos(x) × 1/cos(x)</strong></p><p><strong>y' = tan(x)sec(x)</strong></p><p>&nbsp;</p><p><strong>Sekarang kita tentukan turunan y = csc(x) yang sama dengan :</strong></p><p><strong>y = 1/sin(x)</strong></p><p><strong>u = 1</strong></p><p><strong>u' = 0</strong></p><p><strong>v = sin(x)</strong></p><p><strong>v' = cos(x)</strong></p><p>&nbsp;</p><p><strong>Maka turunan y = csc(x) :</strong></p><p><strong>y' = (0 × sin(x) - 1 × cos(x))/(sin(x))²</strong></p><p><strong>y' = -cos(x)/sin²(x)</strong></p><p><strong>y' = -cos(x)/sin(x) × 1/sin(x)</strong></p><p><strong>y' = -cot(x)csc(x)</strong></p><p>&nbsp;</p><p><strong>Maka kita bisa tentukan turunan :</strong></p><p><strong>y = sec(x) - √8csc(x)</strong></p><p><strong>y' = tan(x)sec(x) - √8(-cot(x)csc(x)</strong></p><p><strong>y' = tan(x)sec(x) + √8cot(x)csc(x)</strong></p><p>&nbsp;</p><p><strong>Jadi hasil turunannya adalah y' = tan(x)sec(x) + √8cot(x)csc(x).</strong></p><p><strong>Semoga membantu!</strong></p><p>&nbsp;</p>