Question

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Answer 1

Answer:

$f'(x) = -\frac{2x}{1 - x^{2}}$

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 $a*x^{n}$ is $a*n*x^{n-1}$. The derivative of $x^{3}$ is $3x^{2}$, for example.

The derivative of the ln function:

If we have:

$y = \ln{g(x)}$

The derivative is

$y' = g'(x)*\frac{1}{g(x)}$

In this problem, we have that:

$y = \ln{1 - x^{2}}$

So $g(x) = 1 - x^{2}$ and $g'(x) = -2x$

So the derivative to this function is

$f'(x) = -\frac{2x}{1 - x^{2}}$