Example2:
Whatis the slopeof the tangentline to the function that passesthroughpointx= 3?
Solution:
We can write This exampleillustratesthe pointthat can be any real number
includingfractions.Usingthe GeneralPowerRule,
To find the slopeof the tangentline, we simplysubstitutex= 3 into the derivative:
Example3:
Finddy/dxfory= sin^3 x.
Solution:
The functioncan be writtenas Thus
Example4:
Finddy/dxfor
Solution:
Let By the chainrule,
where Thus
= 5(-sinu). (6x)