Question #7c49e

1 Answer
Timber Lin
Dec 19, 2017

#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#

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