Answer to Question #331691 in Calculus for Olga

Question

Find the derivative of the function

P(x)=ln ⁡[ (4x + 1)^3 / (2x − 5)^4 ]

is

a. −4(2x−17) / (4x+1)(2x−5)

b.−4(2x−17) / (4x+1)

c. 4(−2x−17) / (4x+1)(2x−5)

d. (−2x−17) / (4x+1)(2x−5)

Answer 1

$P’(x)=(ln ⁡[ (4x + 1)^3 / (2x − 5)^4 ])’= \frac{1}{(4x + 1)^3 / (2x − 5)^4}*((4x + 1)^3 / (2x − 5)^4)’=\frac{(2x-5)^4}{(4x+1)^3}*\frac{12(4x+1)^2*(2x-5)^4-8(2x-5)^3*(4x+1)^3}{(2x-5)^8}=\frac{12(2x-5)-8(4x+1)}{(4x+1)(2x-5)}=\frac{24x-60-32x-8}{(4x+1)(2x-5)}=\frac{4(-2x-17)}{(4x+1)(2x-5)}$