Answer:[tex]\frac{dy}{dx}=7(5x^2+6cosx)^6(10x-6s\imaginaryI nx)[/tex]Explanation:
The given equation is:
[tex]y=(5x^2+6cosx)^7[/tex]
This will be solved using the chain rule method
Let u = 5x² + 6cosx
[tex]\frac{du}{dx}=10x-6sinx[/tex][tex]\begin{gathered} y=u^7 \\ \\ \frac{dy}{du}=7u^6 \end{gathered}[/tex][tex]\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}[/tex][tex]\begin{gathered} \frac{dy}{dx}=7u^6\times(10x-6sinx) \\ \\ \frac{dy}{dx}=7(5x^2+6cosx)^6(10x-6sinx) \end{gathered}[/tex]
