Find the first derivative of the following exponential and logarithmic functions a) y=e^(5x) b) y=xe^(2x) c) y=2^((x-1))

Adrian Brown

Adrian Brown

Answered question

2022-11-09

Find the first derivative of the following exponential and logarithmic functions
a )   y = e 5 x b )   y = x e 2 x c )   y = 2 ( x 1 )

Answer & Explanation

Raven Hawkins

Raven Hawkins

Beginner2022-11-10Added 19 answers

d d x ( e x ) = e x , d d x ( a x ) = a x ln ( a ) d d x ( u v ) = u d v d x + v d u d x
a ) y = e 5 x d y d x = d d x ( e 5 x ) = e 5 x d d x ( 5 x ) = e 5 x 5 = 5 e 5 x
b ) y = x e 2 x d y d x = x d d x ( e 2 x ) + e 2 x d d x ( x ) = x 2 e 2 x + e 2 x 1 = 2 x e 2 x + e 2 x = ( 2 x + 1 ) e 2 x
Rosemary Chase

Rosemary Chase

Beginner2022-11-11Added 4 answers

c ) y = 2 ( x 1 ) = 1 2 2 x d y d x = 1 2 d d x ( 2 x ) = 1 2 2 x ln ( 2 ) = ln ( 2 ) 2 x 1

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