What is the derivative of $y=tan(x)/x$ ?

Question

10434 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-07-23T18:04:03

This function, in the form of $y = f(x) = g(x)/(h(x))$ , is a perfect candidate for using the quotient rule.

The quotient rule states that the derivative of $y$ with respect to $x$ can be solved with the following formula:

Quotient rule: $y'= f'(x) = (g'(x)h(x) - g(x)h'(x))/(h(x)^2)$

In this problem, we can assign the following values to the variables in the quotient rule:

$g(x) = tan(x)$
$h(x) = x$

$g'(x) = sec^2(x)$
$h'(x) = 1$

If we plug these values into the quotient rule, we get the final answer:

$y' = (sec^2(x) * x - tan(x) * 1)/x^2 = (xsec^2(x) - tan(x))/x^2$

What is the derivative of y=tan(x)/xy=tan(x)/x?