Derivatives of Constant Multiples

Example:

H = 3*(2*t)^-1

The first thing to notice when finding the derivative of this function is that it is the product of a constant and another function, as shown in color below:

(2*t)^-1

The Derivative Rule for Constant Multiples:

The derivative of a constant multiple is the constant times thederivative of the function.
If

( f(x) )

then the derivative of z is

	z'	=	( c	f(x) )'
		=	c	f '(x)

So our example,

(2*t)^-1

we can think of as

f(t)

So the derivative is

H '	= (	c	f(t)	)'
	=	c	f '(t)
	=	3	((2*t)^-1)'

and we just need to know the derivative on the right-hand side of the equation. In this case this is

(2*t)^-1

2*(-1)*(2*t)^-2

(by the chain rule)

so the finished derivative is

H '	=	3	( 2(-1)(2*t)^-2 )
	=	(-6)(2t)^-2

additional explanation for the derivative of constant multiples
see another derivative of constant multiples example
practice gateway test
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Page Generated: Sat Apr 19 13:20:42 2025
Comments to Gavin LaRose
glarose@umich.edu
©2001 Gavin LaRose, University of Michigan Math Dept.