Logarithmic Differentiation

What are Logarithmic Functions?

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What is Derivative of Logarithmic Function?

The function that is the inverse of the exponential function is called the logarithmic function. It is represented as logbx, where b is the base of the log. The value of x is the value which equals the base of the logarithm raised to a fixed number y, thus, the general form of a logarithmic function is:...

Derivative of Logarithmic Function Formula

The derivative of the logarithmic functions is solved using the properties of the logarithms and chain rule. It is used to solve complex functions which cannot be solved directly. By using the logarithmic functions, the complex functions can be simplified and can be evaluated easily....

Proof of Derivative of Logarithmic Function Using First Principle

There are three formulas for the derivatives of the logarithmic functions. The following are the formulas for the derivative of the logarithmic functions....

Logarithmic Differentiation

Using the first principle of derivative (d / dx) f(x) = limh→0[{f(x +h) – f(x)} / {(x + h) – x}] Here, f(x) = ln x (d / dx) f(x) = limh→0[{ln(x +h) – ln(x)} / h] ⇒ (d / dx) f(x) = limh→0[{ln{(x +h)/(x)}} / h] ⇒ (d / dx) f(x) = limh→0[{ln(1 + (h / x))} / h] Now, putting (h / x) = (1 /n) and as limit h→0 then, (1 / n) → ∞ (d / dx) f(x) = limn→∞ (n / x) [ln(1 + (1 / n))] ⇒ (d / dx) f(x) = limn→∞ (1 / x) ln(1 + (1 / n))n The value of limn→∞ ln(1 + (1 / n))n = e (d / dx) f(x) = (1 / x) ln e . . . (1) ⇒ (d / dx) ln x = 1 / x For (d / dx) logax = 1 / (x ln a) putting in 1 (d / dx) logax = (1 / x) logae ⇒ (d / dx) logax = (1 / x) ln e /ln a [logae = ln e / ln a ] ⇒ (d / dx) logax = 1 / (x ln a)...

Solved Examples on Derivatives of Logarithmic Function

Logarithmic Differentiation uses the chain rule of differentiation with the differentiation formula of the log, and it helps us differentiate complex functions with ease. There are three forms of logarithmic differentiation i.e., differentiation of ln x, differentiation of logax and differentiation of ln f(x) whose differentiation formulas are mentioned above....

Practice Problems on Differentiation of Logarithmic Function

Example 1: Evaluate:...

Derivatives of Logarithmic Function – FAQs

Problem 1: Calculate the derivative of g(x) = 3ln(2x)....