Question

Derive:

y= 1/3x^2 - 1/4

I came up with -6/x^3

however, the book says that is -2/3x^3.
What am I doing wrong?

Answer 1

1/3x^2 is the same as 1/3* x^(-2).

To derive x to the power of a negative number we use the same rule as x to the power of any positive number.

So that derived is 1/3 * (-2) * x^(-3) which is (-2) / (3*x^3).

Answer 2

so the numerator would be a polynomial: (1) ( 3x^-2) -(1/4) ; 1/4 is a constant so the derivative is 0. So then 3(-2)x^-3 would be -6x^-3 correct? or if you move the negative exponent you end up with what I got -6/x^3

Answer 3

Ooooh I see what you did, ok. So my answer was wrong completely. Wrong, in which part did I make the mistake? Was it wrong to move the denominator first of did I apply the exponent rule wrongfully? @ angusv

Answer 4

No no no silly.
When you change the exponent to negative, you don't bring the 3 up with it!
Yah the exponent rule is where the boo boo is showing up :C

Answer 5

oooooo because the negative exponent only applies to the variable. got it

Answer 6

I haven't been called silly in a long time hahahaha =) thank you!! minor details!!@zepdrix

Answer 7

lol :)