Question

Encontre a derivada de f ( x ) = ( 2 x 4 − 1 ) ( 5 x ³ + 6 x )

Answer 1

Resposta:

f(x) = (2x⁴ - 1).(5x³ + 6x)

f'(x) = [(2x⁴ - 1).(5x³ + 6x)]'

f'(x) = (2x⁴ - 1)'.(5x³ + 6x) + (5x³ + 6x)'.(2x⁴ - 1) ⇒ Utilize a regras:

• (f.g)' = f'.g + g'.f
• (f + g)' = f' + g'
• (axⁿ)' = n.axⁿ⁻¹
• (ax¹)' = a
• (a)' = 0

f'(x) = [(2x⁴)' - (1)'].(5x³ + 6x) + [(5x³)' + (6x)'].(2x⁴ - 1)

f'(x) = (4.2x⁴⁻¹ - 0).(5x³ + 6x) + (3.5x³⁻¹+ 6).(2x⁴ - 1)

f'(x) = (8x³ - 0).(5x³ + 6x) + (15x² + 6).(2x⁴ - 1)

f'(x) = 8x³.(5x³ + 6x) + (15x² + 6).(2x⁴ - 1)

f'(x) = 40x⁶ + 48x⁴ + 30x⁶ - 15x² + 12x⁴ - 6

f'(x) = 70x⁶ + 60x⁴ - 15x² - 6