Question

Find g''(x) for \[g(x)=\frac{2x+1}{5x^2}\]

Answer 1

show your work

Answer 2

\[g'(x)=\frac{5x^2(2)-(2x+1)10x}{(5x^2)^2}\]
\[g'(x)=\frac{10x^2-20x^2-10x}{25x^4}\]\[g'(x)=\frac{-(10x^2+10x)}{25x^4}\]

Answer 3

go ahead

Answer 4

\[g'(x)=\frac{-10x-10}{25x^3}=\frac{-2x-2}{5x^3}\]

Answer 5

Simplify the fraction more before taking the derivative again.

Answer 6

\[g''(x)=\frac{5x^3(-2)-(-2x-2)15x^2}{(5x^3)^2}\]\[g''(x)=\frac{-10x^3+30x^3+30x^2}{25x^6}\]\[g''(x)=\frac{5x^2(-2x+6x+6)}{25x^6}\]\[g''(x)=\frac{-2x+6x+6}{5x^4}=\frac{-2(x-3x-3)}{5x^4}\]

Answer 7

Or, rather...

\[g''(x)=\frac{4x+6}{5x^4}\]

Answer 8

thanks ya'll

Answer 9

Great job!

Answer 10

\[g'(x)=\frac{-2x-2}{5x^3}\]\[g''(x)=\frac{5x^3(-2)-(-2x-2)15x^2}{(5x^3)^2}\]\[g''(x)=\frac{-10x^3+30x^3+30x^2}{25x^6}\]\[g''(x)=\frac{20x^3+30x^2}{25x^6}=\frac{5x^2(4x+6)}{5x^2(5x^4)}\]\[g''(x)=\frac{4x+6}{5x^4}\]