Derivatives?

Question

hello i had a question about this problem finding tangent of this equation with slope(M) when x =3
y = x + (9/x)
pls show the steps

was there a short cut to it?

Answer 1

y = x + 9/x
dy/dx = 1 - 9/x^2
when x=3, dy/dx = 1 - 9/9 = 0 and y = 3 + 9/3 = 6
so equation is given by :
y-6 = 0(x-3)
y-6=0
y=6

Answer 2

i was going to answer this but when i saw lisa's i decided not to her answer is excellent. i didnt look at the arithmetic but her process and the derivaitive are right on so i would say her arithmetic is right on too.