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Find the derivatives :k(x)=(cos(x)∙(3x+1))/(2x^2 )?
2 Answers
- sioiengLv 74 years agoFavorite Answer
k(x)
= [cos(x) ∙ (3x + 1)] / (2x²)
= [(3x + 1) cos(x)] / (2x²)
k'(x)
= {[(3x + 1) cos(x)] / (2x²)}'
= {(2x²) [(3x + 1) cos(x)]' - [(3x + 1) cos(x)] (2x²)'} / (2x²)² …... for (f/g)' = (g f' - f g') / g²
= {(2x²) [(3x + 1) (-sin(x)) + 3 cos(x)] - [(3x + 1) cos(x)] (4x)} / (4x⁴)
= {-6x³ sin(x) - 2x² sin(x) + 6x² cos(x) - 12x² cos(x) - 4x cos(x)} / (4x⁴)
= [-6x³ sin(x) - 2x² sin(x) - 6x² cos(x) - 4x cos(x)] / (4x⁴)
= - 2x [x (3x + 1) sin(x) + (3x + 2) cos(x)] / (4x⁴)
= - [x (3x + 1) sin(x) + (3x + 2) cos(x)] / (2x³)
