Question

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

f(x) = ln(1 - x2)

Answer 1

`f'(x) = -(2x)/(1 - x^(2))`

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)*(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) = -(2x)/(1 - x^(2))`