What is the derivative of ln[(2x-3)/(7x+8)]^(1/2)ln[2x37x+8]12?

1 Answer
May 2, 2018

The answer (1/(2x-3))-(7/(14x+16))(12x3)(714x+16)

Explanation:

show below we will use the properties of ln

ln[(2x-3)/(7x+8)]^(1/2)=1/2*ln[(2x-3)/(7x+8)]ln[2x37x+8]12=12ln[2x37x+8]

1/2*ln[(2x-3)/(7x+8)]=1/2[ln(2x-3)-ln(7x+8)]12ln[2x37x+8]=12[ln(2x3)ln(7x+8)]

1/2ln(2x-3)-1/2ln(7x+8)12ln(2x3)12ln(7x+8)

now the derivative

1/2*(2/(2x-3))-1/2*(7/(7x+8))12(22x3)12(77x+8)

(1/(2x-3))-(7/(14x+16))(12x3)(714x+16)