We have y = (sin x)/ x
=> y = (x^-1) * (sin x)
y' = x^-1 * cos x + sin x * (-1)*x^-2
=> y' = (cos x)/x - (sin x)/x^2
The required value of dy/dx = (cos x)/x - (sin x)/x^2
At a stationary point we have...
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We have y = (sin x)/ x
=> y = (x^-1) * (sin x)
y' = x^-1 * cos x + sin x * (-1)*x^-2
=> y' = (cos x)/x - (sin x)/x^2
The required value of dy/dx = (cos x)/x - (sin x)/x^2
At a stationary point we have dy/dx = (cos x)/x - (sin x)/x^2 = 0
(cos x)/x - (sin x)/x^2 = 0
=> x*(cos x) = sin x
=> x = (sin x)/(cos x)
=> x = tan x.
It is thereby proved that x = tan x at the stationary points of the curve y = (sin x)/x