How do you find the deriverative of the following function?

Question

f(x)=x^2 / x+1

Answer 1

Use the quotient rule:
f'(x)=g(x)f'(x)-g'(x)f(x)/
(g(x))^2
f(x)=x^2
g(x)=x+1
(x+1)(2x)-(1)(x^2)/(x+1)^2
2x^2+2x-x^2/(x+1)^2
x^2+2x/(x+1)^2 or
x(x+2)/(x+1)^2

I hope this helps!

Answer 2

(A more practical suggestion): The quotient formula for derivatives---
F'(u/v) = (v*f'(u) - uf'(v))/v²

For your example, F'(x) = ((x+1)2x - x²(1))/(x+1)²
The numerator can be simplified a bit; I'll let you do that...
.

Answer 3

if f(x) = g(x)/h(x)
then
df/dx = [h(x)*dg/dx - g(x)*dh/dx]/[h(x)]^2
here:
f(x) = x^2/(x+1)
df/dx = [2x(x+1) - x^2]/(x+1)^2 = x(x+2)/(x+1)^2

Answer 4

Use the difference quotient.

f(x)=(f(x+h)-f(x))/h