Question

Find dy/dx and express the final answer with a common denominator

y=ln x^(2(4x-12))

Answer 1

y=ln x^(2(4x-12))

y=ln x^(8x-24)
recall rules of logs, ln a^b = (b)(lna)

y = (8x-24)ln(x)

dy/dx = (8x-24)(1/x) + 8( ln(x) )
= 8 - 24/x + 8lnx
= (8x - 24 + 8x(lnx) )/x