What is the derivative of #-5x#?

2 Answers
Aug 14, 2017

#-5#

Explanation:

now the power rule for differentiation is:

#d/(dx)(ax^n)=anx^(n-1)#

#:.d/(dx)(-5x)#

#=d/(dx)(-5x^1)#

#=-5xx1xx x^(1-1)#

using the power rule

#=-5x^0=-5#

if we use the definition

#(dy)/(dx)=Lim_(h rarr0)(f(x+h)-f(x))/h#

we have

#(dy)/(dx)=Lim_(h rarr0)(-5(x+h)- -5x)/h#

#(dy)/(dx)=Lim_(h rarr0)(-5x-5h+5x)/h#

#(dy)/(dx)=Lim_(h rarr0)(-5h)/h#

#(dy)/(dx)=Lim_(h rarr0)(-5)=-5#

as before

Aug 14, 2017

-5

Explanation:

We can say
#f(x)=-5x#
The derivative of #f(x)# is defined as

#lim_(h->0)(f(x+h)-f(x))/h#

So,

#"The Derivative of f(x)"=lim_(h->0)(-5x-5h-(-5x))/h#

#=lim_(h->0)(-5x+5x-5h)/h#

#=lim_(h->0)(-5h)/h#

#=-5#

Hope it'd help.