Question

For (d/dx) log |e^x [(x – 4)/(x + 4)]^(3/4)| at x = 5 then (dy/dx) =___________

(a) (5/3) 

(b) (3/5) 

(c) – (3/5) 

(d) – (5/3)

Answer 1

The correct option (a) (5/3)   

Explanation:

y = log_e [e^x {(x – 4)/(x + 4)}^(3/4)]

= log_e e^x + (3/4) log_e [(x – 4)/(x + 4)]

y = x + (3/4) [log(x – 4) – log (x + 4)]

∴ (dy/dx) = 1 + (3/4) [{1/(x – 4)} – {1/(x + 4)}]

= 1 + (3/4) [8/(x² – 16)]

= 1 + [6/(x² – 16)]

(dy/dx) = [(x² – 10)/(x² – 16)]

∴ |(dy/dx)|_x=5 = (15/9) = (5/3)