How do you differentiate #y= ln sqrt( 6x^2+8)#?
1 Answer
May 1, 2018
Explanation:
#"differentiate using the "color(blue)"chain rule"#
#"given "y=f(g(x))" then"#
#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#
#rArrdy/dx=1/(sqrt(6x^2+8))xxd/dx(sqrt(6x^2+8))#
#d/dx(sqrt(6x^2+8))=d/dx((6x^2+8)^(1/2))#
#=1/2(6x^2+8)^(-1/2)xxd/dx(6x^2+8)#
#=(6x)/(sqrt(6x^2+8))#
#rArrdy/dx=1/(sqrt(6x^2+8))xx(6x)/(sqrt(6x^2+8))#
#color(white)(rArrdy/dx)=(6x)/(6x^2+8)=(3x)/(3x^2+4)#
