Explanation
[tex]\begin{gathered} y=\left(7x-2\right)\:\left(3x⁴-7\right)^3 \\ \frac{dy}{dx}=\frac{d}{dx}\left((7x-2\right)\:\left(3x⁴-7\right)^3) \\ \mathrm{Apply\:the\:Product\:Rule}:\quad \left(f\cdot g\right)'=f\:'\cdot g+f\cdot g' \\ =\frac{d}{dx}\left(7x-2\right)\left(3x^4-7\right)^3+\frac{d}{dx}\left(\left(3x^4-7\right)^3\right)\left(7x-2\right) \\ =7\left(3x^4-7\right)^3+36x^3\left(3x^4-7\right)^2\left(7x-2\right) \end{gathered}[/tex]Answer:
[tex]7\left(3x^4-7\right)^3+36x^3\left(3x^4-7\right)^2\left(7x-2\right)[/tex]