maths.com >>>> Calculus >>>> Differentiation >>>> The Chain Rule

Calculus

Differentiation Using The Chain Rule

Applied To Exponential Functions Of Type y = e^(kx)
where k is a constant

y = e^(kx)

dy/dx = e^(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 = e^(5x) with respect to x

[1] 'Differentiate with respect to the brackets'

dy
	=	e^(5x)
d(...)

[2] Multiply by the 'inside differential'

dy
	=	e^(5x)	×	5
dx

[3] Simplify

dy
	=	5	×	e^(5x)
dx

dy
	=	5e^(5x)
dx

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

y = e^(5x)

dy
	=	e^(5x)(5)
dx

dy
	=	(5)e^(5x)
dx

dy
	=	5e^(5x)
dx

maths.com Home

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.

Contact

Disclaimer

Privacy

Feedback

Calculus

Differentiation Using The Chain Rule

Applied To Exponential Functions Of Type y = e(kx) where k is a constant

Applied To Exponential Functions Of Type y = e^(kx)
where k is a constant