Find the derivative of the function y ln x42 y Solutiony l

Find the derivative of the function.

y = (ln x⁴)²

y\' =

Solution

y = (lnx^4)^2

Let u =lnv ; v = x^4

y = u^2

dy/dx = (dy/du)(du/dv)(dv/dx)

dy/du = 2u ; dv/dx = 4x^3 ; du/dv = 1/v

dy/dx = ( 2u)(1/v)(4x^3) = (2lnv)(1/x^4)(4x^3)

= (2ln(x^4)(4/x)

= (8/x)ln(x^4)

= ln(x^32)/x