Question

find the derivative of the function g(a), below. it may be to your advantage to simplify before differentiating.
g(a) = tan(arctan(3a))
g(a) =
(your answer should be in simplified form)

Explanation:

Step1: Simplify the function

The functions $\tan(x)$ and $\arctan(x)$ are inverse - functions of each other. For all real numbers $x$, $\tan(\arctan(x))=x$. So, $g(a)=\tan(\arctan(3a)) = 3a$.

Step2: Differentiate the simplified function

The derivative of a function of the form $y = kx$ (where $k$ is a constant) with respect to $x$ is given by the power - rule $\frac{d}{dx}(kx)=k$. Here, $k = 3$ and the variable is $a$. So, $g^{\prime}(a)=\frac{d}{da}(3a)=3$.

Answer:

$3$