# Find the derivative of x/2x+1 with respect to x by quotient rule.

Dear student
$\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{\mathrm{x}}{2\mathrm{x}+1}\right)\phantom{\rule{0ex}{0ex}}=\frac{\left(2\mathrm{x}+1\right)×\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}\right)-\mathrm{x}×\frac{\mathrm{d}}{\mathrm{dx}}\left(2\mathrm{x}+1\right)}{{\left(2\mathrm{x}+1\right)}^{2}}\phantom{\rule{0ex}{0ex}}=\frac{\left(2\mathrm{x}+1\right)\left(1\right)-\left(\mathrm{x}\right)\left(2\right)}{{\left(2\mathrm{x}+1\right)}^{2}}\phantom{\rule{0ex}{0ex}}=\frac{2\mathrm{x}+1-2\mathrm{x}}{{\left(2\mathrm{x}+1\right)}^{2}}\phantom{\rule{0ex}{0ex}}=\frac{1}{{\left(2\mathrm{x}+1\right)}^{2}}$
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