Use logarithmic differentiation to find the derivative of the following equation. y = (6x + 1)5(x4 − 1)6

Question

Use logarithmic differentiation to find the derivative of the following equation.

y = (6x + 1)⁵(x⁴ − 1)⁶

Answer 1

log y = 5 ln (6x+1) + 6 ln (x⁴ - 1)

(1/y) (dy/dx) = 30/(6x+1) + 6/[(x⁴-1)*4x³]

dy/dx = (6x+1)⁵(x⁴-1)*[30/(6x+1)]*{6/[(x⁴-1)*4x³]}