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Calculus

Differentiation Using The Chain Rule

Applied To Exponential Functions Of Type y = ce(kx)
where c and k are constants

y = ce(kx)

dy/dx = ce(kx)(differential of kx)

[1] Differentiate with respect to the brackets as a unit
[2] Multiply by the differential of the inside of the brackets
[3] Simplify

EXAMPLE
Differentiate y = 3e(7x) with respect to x
[1] 'Differentiate with respect to the brackets'     
dy  
= 3e(7x)
d(...)  
[2] Multiply by the 'inside differential'     
dy  
= 3e(7x) × 7
dx  
[3] Simplify     
dy  
= 7 × 3e(7x)
dx  
    
dy  
= 21e(7x)
dx  

A presentation that shows the method and works to avoid error is

y = 3e(7x)

dy  
 =  3e(7x)(7)
dx  

dy  
 =  (7)3e(7x)
dx  

dy  
 =  21e(7x)
dx  

 

 

 

 
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Edited by Dr David Cornelius an Independent Private Maths Tutor with over 25 years of experience and The Secretary of The Association of Tutors in the UK for 15 years.
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