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Help with exponential derivatives?

+2 votes
Find the derivative of
g(x) = 3^(x^2-x)
asked Jan 11, 2013 in CALCULUS by payton Apprentice

1 Answer

+2 votes

Find the derivative of
g(x) = 3^(x^2-x)

Given function g(x) = 3^(x^2-x)

Derivative each side with  respect  " x "

d/ dx ( g(x) ) = d / dx 3^(x^2-x)

g'(x)  =  3^(x^2-x) (ln 3) d / dx (x2-x )                             ( d /dx a^x = a^x ln a )

g'(x) =  3^(x^2-x) (ln 3) ( d / dx (x^2) - d / dx (x) )            ( d / dx ( a -b ) = d / dx (a) - d / dx (b) )

g'(x) = ( ln 3) (3^(x^2-x) ) ( 2x - 1 )      

the derivative of g(x) = 3^(x^2-x) = (ln 3) ( 3^(x^2-x) )  ( 2x - 1 )     
 

answered Jan 11, 2013 by ricky Pupil

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