Just be aware that not all of the forms below are mathematically correct. Using the chain rule, we find that the derivative of ln(4x) is 1/xįinally, just a note on syntax and notation: ln(4x) is sometimes written in the forms below (with the derivative as per the calculations above). (The derivative of ln(4x) with respect to 4x is (1/4x))
#DERIVATIVE OF LOG OF X HOW TO#
How to find the derivative of ln(4x) using the Chain Rule: F'(x) We will use this fact as part of the chain rule to find the derivative of ln(4x) with respect to x. In a similar way, the derivative of ln(4x) with respect to 4x is (1/4x). The derivative of ln(s) with respect to s is (1/s) The derivative of ln(x) with respect to x is (1/x) But before we do that, just a quick recap on the derivative of the natural logarithm. Now we can just plug f(x) and g(x) into the chain rule.
Then the derivative of F(x) is F'(x) = f’(g(x)).g’(x) We can find the derivative of ln(4x) (F'(x)) by making use of the chain rule.įor two differentiable functions f(x) and g(x) Let’s define this composite function as F(x): So if the function f(x) = ln(x) and the function g(x) = 4x, then the function ln(4x) can be written as a composite function. Let’s call the function in the argument g(x), which means: Ln(4x) is in the form of the standard natural log function ln(x), except it does not have x as an argument, instead it has another function of x (4x). Using the chain rule to find the derivative of ln(4x) To perform the differentiation, the chain rule says we must differentiate the expression as if it were just in terms of x as long as we then multiply that result by the derivative of what the expression was actually in terms of (in this case the derivative of 4x). This means the chain rule will allow us to perform the differentiation of the function ln(4x).
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