Question

find the derivative of (x³-6x)(2-4x³)

Answer 1

f(x) = ln(x³ - 6x4)
Apply derivative with respect to x both sides.
f'(x) = d/dx [ ln(x³ - 6x4) ]
Apply formula : ( d/dx )ln[f(x)] = ln[f(x)] ( d/dx )f(x)

= [ 1 / (x³ - 6x4) ] (d/dx )(x³ - 6x4)
= [ 1 / (x³ - 6x4) ] (3x² - 6*4x³)
= [ 1 / (x³ - 6x4) ] (3x² - 24x³)
= (3x² - 24x³) / (x³ - 6x4)
= 3x²( 1 - 8x) / x²(x - 6x²)
= 3( 1 - 8x) / (x - 6x²)
f'(x) = 3( 1 - 8x) / (x - 6x²)