Question

Y = (5x ^ 2 + 6cos(x)) ^ 7 Find 1d * (dy)/(dx)

Answer 1

Answer:
`(dy)/(dx)=7(5x^2+6cosx)^6(10x-6s\imaginaryI nx)`Step-by-step explanation:

The given equation is:

`y=(5x^2+6cosx)^7`

This will be solved using the chain rule method

Let u = 5x² + 6cosx

`(du)/(dx)=10x-6sinx`
`\begin{gathered} y=u^7 \\ \\ (dy)/(du)=7u^6 \end{gathered}`
`(dy)/(dx)=(dy)/(du)*(du)/(dx)`
`\begin{gathered} (dy)/(dx)=7u^6*(10x-6sinx) \\ \\ (dy)/(dx)=7(5x^2+6cosx)^6(10x-6sinx) \end{gathered}`