Question

Apply first principle of differentiation to f(x)=3/1-x^2 to determine its derivative

Answer 1

f(x) = 3/(1 - x^2)
f(x+h) = 3/(1-(x+h)^2)

f(x+h) - f(x) = 3/(1-(x+h)^2) - 3/(1 - x^2)
= (3(1 - x^2) - 3(1 - (x+h)^2 )/( (1 - x^2)(1-(x+h)^2) )
= (3 - 3x^2 - 3 + 3x^2 + 6xh + 3h^2 )/ ( (1 - x^2)(1-(x+h)^2) )
= (6xh + 3h^2)/( (1 - x^2)(1-(x+h)^2) )

dy/dx = lim(f(x+h) - f(x) / h , as h ----> 0
= lim (6xh + h^2) / (h( (1 - x^2)(1-(x+h)^2) ) , as h--->0
= lim (6x + h) / ( (1 - x^2)(1- (x+h)^2) ) , as h ---> 0
= 6x / (1 - x^2)^2

Answer 2

What is denominator?
1?
(1-x)^2 ?
(1 - x^2) ?
Please use parentheses.