Question

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

y = ln(x2 + 3)

Answer 1

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

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
`20x^(10)` is
`200x^(9)`, 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{x^(2) + 3}`

So
`g(x) = x^(2) + 3` and
`g'(x) = 2x`

So the derivative to this function is

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