Find the derivative of the function.
g(x) = ln(3x + 5)
= 1/(3x+5)*d/dx (3x+5)
=3/(3x+5)
To find the derivative of the function g(x), which is ln(3x + 5), we can use the chain rule. The chain rule states that if we have a composition of functions, such as f(g(x)), the derivative is given by the product of the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.
In this case, the outer function is ln(x), and the inner function is 3x + 5.
Let's start by finding the derivative of the outer function, which is ln(x). The derivative of ln(x) with respect to x is 1/x.
Next, let's find the derivative of the inner function, which is 3x + 5. The derivative of 3x + 5 with respect to x is simply 3.
Now, we can apply the chain rule. The derivative of g(x) = ln(3x + 5) is:
g'(x) = (derivative of outer function) * (derivative of inner function)
= (1 / (3x + 5)) * 3
Simplifying this expression, we get:
g'(x) = 3 / (3x + 5)
Therefore, the derivative of the function g(x) = ln(3x + 5) is g'(x) = 3 / (3x + 5).