Derivatives?

Question

Find the derivative of F(x) = 4/(x^2 + 2x + 1)

Explain so I can see what I did wrong. Thanks.

Answer 1

I prefer to write:

F(x) = 4(x² + 2x + 1)ˉ¹

And use chain rule:

F'(x) = -4(x² + 2x + 1)ˉ² (2x + 2)

= -4((x + 1)²)ˉ² 2(x + 1)

= -8(x + 1)/(x + 1)⁴

= -8/(x + 1)³

Answer 2

Use the quotient rule if u want, or the product rule.
Quotient rule:
Derivative of the top times the bottom minus derivative of the bottom times the top ALL over the bottowm squared
(0*(x^2+2x+1) - (2x +2)(4))/(x^2+2x+1)^2
simplifies to:
-(8x+8)/(x^2+2x+1)^2

Answer 3

the denominator can be written as (x+1)^2` F`(x) =4 *1/(x+1)^4 *(-2)(x+1) = -8/(x+1)^3 (rule for deriving a quotient)

Answer 4

derivative of a quotient u/v: (vdu-udv)/(v^2)

u = 4, v = (x^2 +2x +1)

derivative = -4(2x+2) / (x^2 +2x +1)^2

= -8(x+1) / (x+1)^4

= -8 / (x+1)^3

Answer 5

d/dx[4 / (x^2 + 2x + 1)]
= 4 . d/dx[1/(x+1)2]
= 4 . d/dx[(x + 1)^(-2)]
= 4 . (-2)(x + 1)^(-2-1). d/dx(x + 1)
= - 8(x+1)^(-3) (1)
= - 8 /(x + 1)^3

Answer 6

you need to factor out (x^2+2x+1)

(x+1)(x+1)

i believe thats the derivative? (x+1)

Answer 7

This is a quotient, so use the quotient rule.

To differentiate the denominator, use the addition and constant multiplier rules.

And be cautious. Good luck.