How to Convert Notation for Differentiating Functions?

[fitz_calc]

Homework Statement

differentiate the given function: y=2/x^2 -1/x^3 +1/2^3

Homework Equations

The Attempt at a Solution

2(-2x^3) -1(-3x^4)
-4x^3 + 3x^4

my book says the answer is:

how do you go from my notation to the one my book uses?

 

[bel]

I think instead of positive indices, you should have negative indices, then the step is obvious.

 

[bob1182006]

yes it's not x^2 it's x^(-2) and the same with x^3 should be x^(-3) since it's a fraction.

 

[fitz_calc]

yes it's not x^2 it's x^(-2) and the same with x^3 should be x^(-3) since it's a fraction.

ahh I used the power incorrectly, yes the exponents should both be negative. i know there is some algebra rule that states if your exponent is negative then put the x value and exponent in the denominator -- what rule is this?

 

[fitz_calc]

*here's another example:

y+1/3sqrt(x)

i get: -1/3(x^4/3)

Book:

why does the x^4/3 get put in the denominator?

 

[rocomath]

*here's another example:

y+1/3sqrt(x)

i get: -1/3(x^4/3)

Book:

why does the x^4/3 get put in the denominator?

can you re-type that please.

y+?

 

[rocomath]

ahh I used the power incorrectly, yes the exponents should both be negative. i know there is some algebra rule that states if your exponent is negative then put the x value and exponent in the denominator -- what rule is this?

$$\frac{1}{a^n}=a^{-n}$$

$$\frac{a^{-n}}{b^{-m}}=\frac{b^{m}}{a^{n}}$$

 

[drpizza]

If you follow what rocophysics laid out for you, and rewrite your original function before attempting to take the derivative, then you'll simply need to use the power rule for finding the derivative.

If you want to leave those x's in the denominator and not use the power rule, then you'll have to use the quotient rule instead (which you'll probably learn very soon.) In this case though, the power rule requires much less thought.

 

[fitz_calc]

cool, thanks!