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Step-by-step Solution

Find the higher order derivative of $\ln\left(x\right)$

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Step-by-step explanation

Problem to solve:

$\frac{d^3}{dx^3}\left(\ln\left(x\right)\right)$

Learn how to solve differential calculus problems step by step online.

$\frac{d^{2}}{dx^{2}}\left(\frac{d}{dx}\left(\ln\left(x\right)\right)\right)$

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Learn how to solve differential calculus problems step by step online. Find the higher order derivative of ln(x). Rewriting the high order derivative. Rewriting the high order derivative. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. Applying the quotient rule which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}.

Answer

$\frac{2}{x^{3}}$

Problem Analysis

$\frac{d^3}{dx^3}\left(\ln\left(x\right)\right)$

Main topic:

Differential calculus

Related formulas:

4. See formulas

Time to solve it:

~ 0.09 seconds