Question

Question #7c49e

Answer 1

`9/20`

Explanation:

the slope is given by `y'(4)` where `y'(x)` is the derivative of `y=ln(x^2+x)` with respect to x.

`y'(x)=d/dx(ln(x^2+x))`
`y'(x)=(1/(x^2+x))(d/dx(x^2+x))` (ln(x) derivative and chain rule)
`y'(x)=1/(x^2+x)*(2x+1)` (power rule)

now evaluate at `x=4`:
`y'(4)=(1/((4)^2+(4)))*(2(4)+1)`

`y'(4)=(1/20)*(9)=9/20`