Find dy/dx. y= 4 ln x + 9 log 4x

Question

Find dy/dx.

y= 4 ln x + 9 log ₄x

dy/dx= ____________ ​(Type an exact​ answer.)

Answer 1

y = 4lnx + 9log4(x)

y = 4lnx + 9lnx/ln4

y' = 4/x + 9/xln4

dy/dx = y' = 4/x + 9/xln4

(derivative of logb(x) = 1/xln(b) and derivative of lnx =1/x)

Answer 2

y= 4 ln(x) + 9 log₄₍x)

= 4ln(x) + (9/ln(4))ln(x)

dy/dx = 4/x + 9/(xln(4))

Answer 3

dy/dx = 4·1/x + 9·1/(4x)·4/ln10 = 4/x + 9/(xln10)