Question #7c49e

1 Answer
Dec 19, 2017

9/20920

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