find the derivative of the function g(a), below. it may be to your advantage to simplify before…

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

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

Answer

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:

$3$