Question

y=sin(2x)/x, x=Pi, dx=.25

find the differentiate

Answer 1

$\frac{dy}{dx}=\frac{2cos(2x)}{x}-\frac{sin(2x)}{x^2}.$

$dy=[\frac{2cos(2x)}{x}-\frac{sin(2x)}{x^2}]dx.$

When $x=\pi, \;dx=0.25:$

$dy=[\frac{2cos(2\pi)}{\pi}-\frac{sin(2\pi)}{\pi^2}]*0.25=\frac{0.5}{\pi}\approx 0.1592.$