# calculus

posted by .

Using the 4 step method fidn the derivative of F(x) =1/(x^2)

1) I got /(x^2+2xh+h^2)
2)2xh+h^2/(x^2+2xh+h^2)(x^2)
3)2x+h/(x^2+2xh+h^2)(x^2)
4)1/x

I don't understand why I got this problem wrong on my test can you explain the correct way?

The second step is wrong, it should be lim h->0 [F(x+h)-F(x)]/h
So we should have
lim h->0 1/(x^2+2xh+h^2) - 1/x^2 =
lim h->0 [x^2 - (x^2+2xh+h^2)]/[h*(x^2+2xh+h^2)*x^2] =
lim h->0 -(2xh+h^2)/[h*(x^2+2xh+h^2)*x^2] =
lim h->0 -(2x+h)/[(x^2+2xh+h^2)*x^2] =
lim h->0 -(2x+h)/(x^4+2x^3h+x^2h^2) =
-2x/x^4 =
-2/x^3 = F'(x)

## Similar Questions

1. ### Calculus (Help)

Also I would like to know how to set this problem up in finding the answer: Find the second derivative. y= sqrt(3x+4) Thanks, P.S. I tried taking 3x+4 and squaring it to the 1/2. I thought that might've been the same, then I took the …
2. ### Algebra

I don't understand how to do the folliwing problems. Find and simplify the difference quotient f(x+h) -f(x)/h, h cannot equal 0 for the given formula. 1. f(x)=5x^2 options: a. 5, b.5(2x+h), c. 10/h +x+5h, d. 5(2x^2+2xh+h^2)/h 2. f(x)=x^2+3x+9 …
3. ### Algebra

I don't understand how to do the folliwing problems. Find and simplify the difference quotient f(x+h) -f(x)/h, h cannot equal 0 for the given formula. 1. f(x)=5x^2 options: a. 5, b.5(2x+h), c. 10/h +x+5h, d. 5(2x^2+2xh+h^2)/h 2. f(x)=x^2+3x+9 …
4. ### calculus

Difference Quotient of x^2-2x (x+h)^2-2(x+h)-(x^2-2x) / h x^2+2xh+h^2-2x-2h-x^2+2x / h x^2 cancel out 2x cancel out h and -2h cancel and leave -2 result: h^2+2xh-2
5. ### Math

How would you simplify (-x^2+2xh+h^2-2x-2h-2x^2+4x)/h ?
6. ### Maths

differentiate from first principles y=1/x^2 i get to this then i get stuck f(x+h)-f(x) = 1/(x+h)^2 - 1/x^2 = x^2 - x^2 -2xh -h^2 above divided by(x^2+2xh+h^2)(x^2) = -2xh -h^2/x^4+2x^3h+h^2x^2 then i know i need to divide by h but …
7. ### calculus

i tried to find the derivative of this questions but it was way too hard, and i got it wrong on a test.. i need help y=x4/3 - (sqr.root)5x + 4/x
8. ### Calculus

1/a+1 + 1/a-1 I solved this out by multiplying the (a+1) by (a-1) and multiplying (a-1) with (a+1) To get (a+1)(a-1) as the denominator. Then I did the same with the numerators and got this: 1(a-1) + 1(a+1)/(a+1)(a-1) And I got 2a/(a+1)(a-1) …
9. ### Math

Find and Simplify. f(x) = 5 − x^2 a)f(x + h) − f(x) b)(f(x + h) − f(x))/h a) I got 2xh+h^2 b) I got 2xh+h I don't know what is wrong, but the answer is incorrect. Thank you.
10. ### Calc 1 limits

Lim h-----> 0. (X+h)^3-x^3/h So I foiled out the numerator And I got X^3 +x^2h +2x^2h +2xh^2+h^2+h^3-x^3 So I canceled out x^3 and -x^3 Then I took out the h from the numerator to cancel out the h in the denominator and then I put …

More Similar Questions