How do you find the derivative of $sinx/x$ ?

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Answer 1 · 2015-04-16T19:12:09

Quotient Rule
$h(x) = f(x)/g(x)$
$h'(x) = (g(x)*f'(x) - f(x)*g'(x))/((g(x))^2)$

$h(x) = sinx/x$
$h'(x) = (x*(sinx)' - sinx*(x)')/(x^2) = (xcosx - sinx)/x^2$
$= cosx/x - sinx/x^2$

Product Rule
$h(x) = f(x)*g(x)$
$h(x) = f(x)*g'(x) + g(x)*f'(x)$

$h(x) = 1/x*sinx$
$h'(x) = 1/x*(sinx)' + sinx*(1/x)' = cosx/x - (sinx)/x^2$

As you can see, you still get the same result in the end.

How do you find the derivative of sinx/xsinx/x?