How do you differentiate y= ln sqrt( 6x^2+8)?

1 Answer
Jim G.
May 1, 2018

dy/dx=(3x)/(3x^2+4)

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)

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