Find f'(x)
f (x) = 4ln(3x + 5)
Using the chain rule:
f'(x) = 4 * (1 / (3x + 5)) * 3
Simplifying:
f'(x) = 12 / (3x + 5)
To find the derivative of f(x) = 4ln(3x + 5), we can use the chain rule.
Step 1: Identify the outer function and the inner function.
The outer function is ln(x) and the inner function is 3x + 5.
Step 2: Find the derivative of the outer function ln(x).
The derivative of ln(x) is 1/x.
Step 3: Find the derivative of the inner function 3x + 5.
The derivative of 3x + 5 is 3.
Step 4: Apply the chain rule.
To apply the chain rule, we multiply the derivative of the outer function by the derivative of the inner function.
f'(x) = (1/(3x + 5)) * 3
Simplifying further, we get:
f'(x) = 3/(3x + 5)
Therefore, the derivative of f(x) = 4ln(3x + 5) is f'(x) = 3/(3x + 5).