1. y = sin (2x - 5)
2. y = cos (x^2 +3x-2)
3. y = tan (5x^2+4)
mohon bantuannya
Penjelasan dengan langkah-langkah:
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TURUN FUNGSI TRIGONOMETRI
Turunan fungsi aljabar
[tex]\boxed{\rm f(x) = ax^n \Rightarrow f^{\prime}(x) = anx^{n - 1}}[/tex]
Turunan fungsi aljabar
[tex]\boxed{\begin{aligned} \rm y & = \rm \sin x \Rightarrow y^{\prime} = \cos x \\ \rm y & = \rm \cos x \Rightarrow y^{\prime} = - \sin x \\ \rm y & = \rm \tan x \Rightarrow y^{\prime} = \sec^2 x \end{aligned}}[/tex]
Menentukan turunan fungsi trigonometri berbentuk f(u)
[tex]\boxed{\begin{aligned} \rm y & = \rm \sin f(u) \Rightarrow y^{\prime} = f^{\prime}(u) \cos f(u) \\ \rm y & = \rm \cos f(u) \Rightarrow y^{\prime} = - f^{\prime} (u) \sin f(u) \\ \rm y & = \rm \tan f(u) \Rightarrow y^{\prime} = f^{\prime}(u) \sec^2 f(u) \end{aligned}}[/tex]
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Soal no. 1
[tex]\rm y = \sin (2x - 5)[/tex]
Misal: [tex]\rm f(u) = 2x - 5 \Rightarrow f^{\prime}(u) = 2[/tex]
[tex]\begin{aligned}\rm y^{\prime} & = \rm f^{\prime} (u) \cos f(u) \\ & = \rm 2 \cos (2x - 5) \end{aligned}[/tex]
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Soal no. 2
[tex]\rm y = \cos (x^2 + 3x - 2)[/tex]
Misal: [tex]\rm f(u) = x^2 + 3x - 2 \Rightarrow f^{\prime} (u) = 2x + 3 [/tex]
[tex]\begin{aligned}\rm y^{\prime} & = \rm - f^{\prime} (u) \sin f(u) \\ & = \rm (2x + 3) \sin (x^2 + 3x - 2) \end{aligned}[/tex]
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Soal no. 3
[tex]\rm y = \tan (5x^2 + 4)[/tex]
Misal: [tex]\rm f(u) = 5x^2 + 4 \Rightarrow f^{\prime} (u) = 10x[/tex]
[tex]\begin{aligned}\rm y^{\prime} & = \rm f^{\prime} (u) \sec^2 f(u) \\ & = \rm 10x \sec^2 (5x^2 + 4) \end{aligned}[/tex]
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