Question

how to derive ln(x^2+5x)

Answer 1

To derive ln(x^2 + 5x), you need to use the chain rule.

Let y = ln(x^2 + 5x).

First, apply the chain rule by finding the derivative of the inside function (x^2 + 5x).

Let u = x^2 + 5x.

Now, find the derivative of u with respect to x:

du/dx = d/dx(x^2) + d/dx(5x)
du/dx = 2x + 5

Now, apply the chain rule to find dy/du:

dy/du = 1/(u)

Now, put it all together to find dy/dx:

dy/dx = dy/du * du/dx
dy/dx = (1/(x^2 + 5x))(2x + 5)

Therefore, dy/dx = (2x + 5)/(x^2 + 5x) is the derivative of ln(x^2 + 5x).