Answer:
[tex]f'(x) = -\frac{2x}{1 - x^{2}}[/tex]
Step-by-step explanation:
The derivative of an addition/subtraction of terms is the addition/subtraction of the derivatives of these terms.
The derivative of a constant is 0.
The derivative of [tex]a*x^{n}[/tex] is [tex]a*n*x^{n-1}[/tex]. The derivative of [tex]x^{3}[/tex] is [tex]3x^{2}[/tex], for example.
The derivative of the ln function:
If we have:
[tex]y = \ln{g(x)}[/tex]
The derivative is
[tex]y' = g'(x)*\frac{1}{g(x)}[/tex]
In this problem, we have that:
[tex]y = \ln{1 - x^{2}}[/tex]
So [tex]g(x) = 1 - x^{2}[/tex] and [tex]g'(x) = -2x[/tex]
So the derivative to this function is
[tex]f'(x) = -\frac{2x}{1 - x^{2}}[/tex]
