Question

Differentiate y = (7x-2) (3x⁴-7) ³

Answer 1

Step-by-step explanation

`\begin{gathered} y=\left(7x-2\right)\:\left(3x⁴-7\right)^3 \\ (dy)/(dx)=(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' \\ =(d)/(dx)\left(7x-2\right)\left(3x^4-7\right)^3+(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}`

Answer:

`7\left(3x^4-7\right)^3+36x^3\left(3x^4-7\right)^2\left(7x-2\right)`