Question

the function $f(x)=\frac{3x}{8 - \tan(x)}$ is a quotient, so well need to use the quotient rule, which states that $\frac{d}{dx}\frac{f(x)}{g(x)}=\frac{g(x)f(x)-f(x)g(x)}{(g(x))^{2}}$. recall that the derivative of $\tan(x)$ is. (its important to simply memorize the derivatives of all six trigonometric functions.)

Explanation:

Step1: Recall derivative of tangent

The derivative of $\tan(x)$ is $\sec^{2}(x)$.

Answer:

$\sec^{2}(x)$