Question

Buna, ma puteti ajuta la problemele urmatoare?

Answer 1

Explicație pas cu pas:

a)

f'(x) = (5x⁴)' - (6x³)' + (3x)' - 4' = 4×5x³ - 3×6x² + 3×x⁰ - 0 = 20x³ - 18x² + 3

b)

$f'(x) = \bigg(\dfrac{ {x}^{2} - 3}{x - 4}\bigg)' = \dfrac{ ({x}^{2} - 3)'(x - 4) - ( {x}^{2} - 3)(x - 4)'}{ {(x - 4)}^{2} } = \\ = \dfrac{2x(x - 4) - ( {x}^{2} - 3) \cdot 1}{ {(x - 4)}^{2} } = \dfrac{2 {x}^{2} - 8x - {x}^{2} + 3}{ {(x - 4)}^{2} } = \dfrac{{x}^{2} - 8x + 3}{ {(x - 4)}^{2} }$

unde:

(x² - 3)' = (x²)' - 3' = 2x¹ - 0 = 2x

(x - 4)' = x' - 4' = 1 - 0 = 1