- WE WANT TO DETERMINE 
THE DERIVATIVE
OF THE GIVEN
EXPONENTIAL FUNCTION.
THE FIRST THING WE SHOULD NOTICE 
IS THAT WE DO HAVE
A COMPOSITE FUNCTION 
WHERE THE INNER FUNCTION
IS 2X TO THE 2ND + 3.
SO WE WILL HAVE TO APPLY 
THE CHAIN RULE
TO DIFFERENTIATE THIS FUNCTION.
SO WE'LL USE 
THIS DERIVATIVE FORMULA
TO DETERMINE F PRIME OF X.
NOTICE THE BASE 
IS EQUAL TO "A,"
SO "A" IS EQUAL TO 7 
IN THIS PROBLEM.
AND THEN OUR INNER FUNCTION 
OR U IS GOING TO BE EQUAL
TO 2X SQUARED + 3.
OUR EXPONENT IS U.
NOW, WE'RE ALSO GOING TO NEED 
U PRIME OR DUDX,
WHICH WOULD BE 4X.
NOW THAT WE HAVE ALL OF THIS 
INFORMATION WE CAN REWRITE
THE FUNCTION IN TERMS OF U.
IT'S GOING TO BE 2 x 7 
TO THE POWER OF U.
SO F PRIME OF X 
IS GOING TO BE EQUAL
TO 2 x THE DERIVATIVE OF 7 
TO THE POWER OF U,
WHICH IS NATURAL LOG "A" x "A" 
TO THE U x U PRIME.
SO WE'LL HAVE 
NATURAL LOG 7 x "A" TO THE U,
WHICH IS GOING TO BE 7 RAISED 
TO THE POWER OF 2X TO THE 2ND
+ 3 x U PRIME WHICH IS 4X.
SO LET'S REWRITE THIS AS--WELL, 
2 x 4X WOULD BE 8X.
SO WE'LL HAVE 8X NATURAL LOG 7 
x OUR EXPONENTIAL FUNCTION
OF 7 TO THE POWER OF 2X 
TO THE 2ND + 3.
IN THE NEXT VIDEO WE'LL TAKE 
A LOOK AT A FUNCTION
THAT'S GOING TO REQUIRE 
THE PRODUCT RULE,
AS WELL AS A DERIVATIVE 
OF AN EXPONENTIAL FUNCTION.
I HOPE THIS WAS HELPFUL.
