Greetings,

Question

So I've been working on this problem:
H(x) = (x^4 - 2x +7)(x^-3 + 2x^-4)
H'(x)=
Kept on getting it wrong and I assumed it was an algebra mistake. After multiple tries I went to a few derivative calculators to check my work...
What I saw was the calculators converted the problem to:

((x+2)*(x^4 -2x +7))/x^4

How exactly do I get from the first equation to the second?

Answer 1

When there is a negavtive exponent you need to flip the term to makee it positive so the problem should be written as:
H(x)=(x^4-2x+7)[(1/x^3)+(2/x^4)]

Then you simply multiply the two groups to get:
H(x)=[(x^4-2x+7)/(x^3)]+[2(x^4-2x+7)/(x^4)]

Then simplify the second fraction to get:
H(x)=[(x^4-2x+7)/(x^3)] + (2x^4/x^4) - (4x/x^4) + (14/x^4)
H(x)=[(x^4-2x+7)/(x^3)] + 2 - (4/x^3) + (14/x^4)

Then sort by order of highest exponent to lowest and your final answer is:
H(x)=(14/x^4) -(4/x^3) +[(x^4-2x+7)/(x^3)] + 2

Answer 2

Whew

[(1/x^3)+(2/x^4)] = x/x^4 + 2/x^4 = (x+2)/x^4