Differentiate: y= 3X/X^2+1?

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Differentiate: y= 3X/X^2+1?

2006-10-02 14:47:27 · 2 answers · asked by j a 1 in Science & Mathematics ➔ Mathematics

2 answers

d/dx[f(x)/g(x)]=

(g(x)*f'(x)-f(x)*g'(x))
-------------------------
g(x)^2

f(x)=3x
f'(x)=3
g(x)=x^2 + 1
g'(x)=2x

2006-10-02 15:29:20 · answer #1 · answered by Inya 3 · 0⤊ 0⤋

y = (3x)/(x^2 + 1)

y' = ((x^2 + 1)(3x)') - ((x^2 + 1)'(3x))/((x^2 + 1)^2)
y' = (3(x^2 + 1) - ((3x)(2x)))/((x^2 + 1)(x^2 + 1))
y' = (3x^2 + 3 - 6x^2)/(x^4 + x^2 + x^2 + 1)
y' = (-3x^2 + 3)/(x^4 + 2x + 1)

2006-10-02 15:05:42 · answer #2 · answered by Sherman81 6 · 0⤊ 0⤋