Derivatives of Constant Multiples

Example:

V = Q*tan(N*y)

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:

tan(N*y)

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,

tan(N*y)

we can think of as

f(y)

So the derivative is

V '	= (	c	f(y)	)'
	=	c	f '(y)
	=	Q	(tan(N*y))'

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

tan(N*y)

N*1 / (cos(N*y))²

(by the chain rule)

so the finished derivative is

V '	=	Q	( N1 / (cos(Ny))² )
	=	(QN)1 / (cos(Ny))²

additional explanation for the derivative of constant multiples
see another derivative of constant multiples example
practice gateway test
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Comments to Gavin LaRose
glarose@umich.edu
©2001 Gavin LaRose, University of Michigan Math Dept.