Question

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

Answer 1

Answer:

$y = \frac{2x}{x^{2} + 3}$

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 $20x^{10}$ is $200x^{9}$, for example.

The derivative of the ln function:

If we have:

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

The derivative is

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

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

$y = \frac{2x}{x^{2} + 3}$