- #1
Specter
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Homework Statement
Find the derivative of the following functions.
h(x)=8x2√x2+1
Homework Equations
The Attempt at a Solution
I just had a lesson on friday but it was a bit confusing to me. I am able to solve some problems but ones that contain multiple rules confuse me. If someone could break down or explain what is happening in this question to me that would be great. This question is solved in the lesson but I don't really know what is happening in each step.
h(x)=8x2√x2+1
h'(x)=8x2(x2+1)1/2
So I understand that √x+1 is now written as x2+11/2
h'(x)=16x(x2+1)1/2(8x2)1/2(x2+1)-1/2(2x)
I understand that 8x2 is now 16x (2*8x=16x). I know that the 1/2 is brought down and then the (x2+1)1/2 becomes (x2+1)-1/2 because (x2+1)1/2-2/2. Next the deriative of x2 is put down at the end but I don't really know why or what rule that is. From here on out I'm pretty lost on what is happening...
=16x(x2+1)1/2+8x3/(x2+1)1/2
=16x3+16x+8x3/(x2+1)1/2
=24x3+16x/√x2+1