Carilah turunan pertama f'(x) dari fungsi f(x) = (5 - x^3)(x^2 - x)
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Jawaban:
f’(x) = –5x⁴ + 4x³ + 10x – 5
Penjelasan:
Turunan
f(x) = (5 – x³)(x² – x)
Jika f(x) = g(x)·h(x), maka:
f’(x) = g’(x)·h(x) + g(x)·h’(x)
Sehingga, untuk f(x) = (5 – x³)(x² – x):
f’(x) = (5 – x³)’·(5 – x³) + (5 – x³)·(x² – x)’
⇔ f’(x) = –3x²(x² – x) + (5 – x³)(2x – 1)
⇔ f’(x) = –3x⁴ + 3x³ + 10x – 2x⁴ – 5 + x³
⇔ f’(x) = –3x⁴ – 2x⁴ + 3x³ + x³ + 10x – 5
⇔ f’(x) = –5x⁴ + 4x³ + 10x – 5
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