Tentukan fungsi turunan berikut

Tentukan fungsi turunan berikut

Jawab:

Penjelasan dengan langkah-langkah:

1. f(x) = 3 $x^{4}$ -6x³+2x²-x+2

f'(x) = 4×3 x³ – 3×6 x² + 2×2 x – 1 + 0

= 12x³-18x²+4x-1

2. f(x) = $frac{1}{3}x^{frac{1}{3} } - frac{2}{5}x^{frac{1}{2} }$

f'(x) = $frac{1}{3}(frac{1}{3})x^{frac{1}{3}-1} - frac{1}{2}(frac{2}{5})x^{frac{1}{2} -1}$

= $frac{1}{9}x^{-frac{2}{3}} - frac{1}{5}x^{-frac{1}{2}}$

f'(x) = $frac{1}{9sqrt[3]{x^{2}}} - frac{1}{5sqrt{x}}$

3. f(x) = 3x²-2x+1

f'(x) = 2×3x – 2 = 6x – 2

4. f(x) = 2(1-x)²

f'(x) = 2×2(1-x) (1) = 4(1-x) = 4 – 4x

5. f(x) = (2x+1)³

f'(x) = 3(2x + 1)² (2) = 6 (2x+1)²