If f(x)=[x+1/x−1]3 then f'(2)= ?
f′(x)=3[x+1/x−1]2just not sure what to do after that
Remember...
ddxu3=3u2⋅ddxu
So
f′(x)=3[x+1x−1]2⋅ddx[x+1x−1] f′(x)=3[x+1x−1]2⋅[ddxx+ddx1x−ddx1] f′(x)=3[x+1x−1]2⋅[1−x−2]
To find f'(2) , plug in 2 for x .
f′(2)=3[2+12−1]2⋅[1−2−2] f′(2)=3[32]2⋅[1−14] f′(2)=3[94]⋅[34] f′(2)=8116
( If f(x) is meant to be [x+1x−1]3 then you get a different answer. )