Q.Differentiate the function $\dfrac{1 - 3x}{1 + 3x}$ with respect to $x$.

By the quotient rule, $\dfrac{d}{dx}\dfrac{1-3x}{1+3x}=\dfrac{(-3)(1+3x)-(1-3x)(3)}{(1+3x)^{2}}=\dfrac{-6}{(1+3x)^{2}}$.

This is a direct application of the quotient rule from the Differential Calculus chapter of the TN HSC Class-11 Business Mathematics syllabus.

Step 1 — Identify $u$ and $v$.

$u=1-3x\Rightarrow u'=-3;\qquad v=1+3x\Rightarrow v'=3.$

Step 2 — Quotient rule.

$\dfrac{d}{dx}\left(\dfrac{u}{v}\right)=\dfrac{u'v-uv'}{v^{2}}.$

Step 3 — Substitute. …