Use logarithmic differentiation to find the derivative of the function. y=(4x+1)^5(x^4-3)^6. y'=?

Answer 1

lny = 5ln(4x + 1) + 6ln(x⁴ - 3)

Differentiate both sides, we get: y'/y = 5/(4x + 1)·4 + 6/(x⁴ - 3)·4x³;

from here y' = [20/(4x + 1) + 24x³/((x⁴ - 3)]·(4x + 1)⁵(x⁴ - 3)⁶