[tex]y=(5x^3+2)\placeholder{⬚}^2[/tex]
General power rule:
[tex]\frac{d}{dx}u^n=nu^{n-1}[/tex]
1. Use the change rule as follow:
[tex]\begin{gathered} u=5x^3+2 \\ \\ y^{\prime}=\frac{d}{du}u^2*\frac{d}{dx}(5x^3+2) \\ \\ y^{\prime}=\frac{d}{du}u^2*(\frac{d}{dx}5x^3+\frac{d}{dx}2) \end{gathered}[/tex]
2. Use the general power rule:
[tex]\begin{gathered} y^{\prime}=2u(15x^2+0) \\ \\ y^{\prime}=2u(15x^2) \end{gathered}[/tex]
3. Substitute u by its value and simplify:
[tex]\begin{gathered} y^{\prime}=2(5x^3+2)(15x^2) \\ y^{\prime}=30x^2(5x^3+2) \\ y^{\prime}=150x^5+60x^2 \end{gathered}[/tex]
Then, the derivate of the given function is:
[tex]y^{\prime}=150x^5+60x^2[/tex]
