Question

Find ds/dt , what will be answer, step by step?​

Answer 1

Answer:

              96t³ + 72 t

Solution,

                $s=(2t+4t^3) \ . \ (6t+\frac{6}{t})$

According to product rule,

                $\frac{d(uv)}{dx} = u\ . \ \frac{d}{dx}(v) \ + v \ . \ \frac{d}{dx}(u)$

∴              $\frac{ds}{dt} = (2t +4t^3) \ . \ \frac{d}{dx}(6t + \frac{6}{t}) \ + (6t + \frac{6}{t}) \ . \ \frac{d}{dx} (2t +4t^3)$

           ⇒ $\frac{ds}{dt} = (2t + 4t^3) \ . \ (6 +\frac{-6}{t^2}) + (6t + \frac{6}{t}) \ .\ (2 + 12t^2)$

If we simplify these terms, we will get the answer,

                 ⇒96t³ + 72 t

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