I am a second year Economics student at the University of Bristol and a keen mathematics enthusiast! I have had the pleasure of tutoring for three years now and have had an excellent record of helping many students get the highest grade achievable!
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Layla (Parent) May 10 2016
As in every case dy/dx can be found by differentiating each term individually with respect to x.
Let's first tackle the 4x term.
As always the derivative can be found by multiplying the term by the power of x and reducing the power of x by 1. i.e. axb -> abxb-1
In this case b is simply equal to 1 because x=x1. Therefore the derivative of 4x with respect to x is given by 1*4x0 = 4*1 = 4.
Next let's tackle the 1/x2 term.
In order to use the same method as previously we must first write 1/x2 as a power of x i.e. in the familiar form axb.
From the laws of indices: recall that x-b=1/xb. In this example b is simply equal to 2 so 1/x2=x-2.
Now that we have written the term in the form axb we can apply the same method as previously i.e. x-2-> -2x-3.
Finally collecting both the terms we have arrived at the result that dy/dx is -2x-3+4.see more