If #f(x)=x^(-5/7)#, how do you compute f'(3)?

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Answer 1 · 2018-04-29T22:17:30

#~~-0.109#

Here, we can use the Power Rule

#d/dx(x^a)=ax^(a-1)#

If this looks foreign to you, it's really straightforward:

Doing this, we get

#-5/7x^(-5/7-7/7)#

#=>f'(x)=-5/7x^(-12/7)#

Now, we can plug in #3# for #x# to evaluate #f'(3)#. We get

#f'(3)=-5/7(3)^(-12/7)#

#=>-5/7*(1/3^(12/7))#

which is approximately equal to #-0.109#

Notice, we only used the Power Rule here, stated above, and we evaluated the expression at #3#.

Hope this helps!