Answer
${dy}={4{x^2}}\sec^2({\frac{{x}^3}{3}}){dx}$
Work Step by Step
We evaluate the function: $y=4\tan(\frac{{x}^3}{3})$
on differentiating the above:
$\frac{dy}{dx}=\frac{d(4\tan(\frac{{x}^3}{3}))}{dx}$
or $\frac{dy}{dx}=4\sec^2(\frac{{x}^3}{3})\frac{d\frac{{x}^3}{3}}{dx}$
or $\frac{dy}{dx}=4\frac{3x^2}{3}\sec^2(\frac{{x}^3}{3})$
or ${dy}={4{x^2}}\sec^2({\frac{{x}^3}{3}}){dx}$
The final answer is: ${dy}={4{x^2}}\sec^2({\frac{{x}^3}{3}}){dx}$
