Solution:
It is possibleto provethis relationby the definitionof the derivative.However, we use a simplermethod.
Since
then
Example2:
Find.
Solution:
Usingthe productrule and the formulasabove,we obtain
Example3:
Finddy/dxif. Whatis the slopeof the tangentline atx= π/3?
Solution:
Usingthe quotientrule and the formulasabove,we obtain
To calculatethe slopeof the tangentline, we simplysubstitutex= π/3: