The equation of the derivative of a function
is written as
where
The notation
is read as “
” Alternate notations for the derivative include the following:
The expression
is now a function of
; this function gives the slope of the curve
at any value of
The derivative of a function
at a point
is denoted
Given a function
find the derivative by applying the definition of the derivative.
To find derivatives of functions with roots, we use the methods we have learned to find limits of functions with roots, including multiplying by a conjugate.
Finding the derivative of a function with a root
Find the
derivative of the function
at
We have
Multiply the numerator and denominator by the conjugate:
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