Logarithmic differentiation and successive differentiation

Logarithmic Differentiation: Logarithmic differentiation is a technique used to find the derivative of a function that is itself a logarithmic function. Thi...

Logarithmic Differentiation:

Logarithmic differentiation is a technique used to find the derivative of a function that is itself a logarithmic function. This is particularly useful when the function has a "logarithmic" or "exponential" function as its base.

Consider the function:

$f(x) = \log(x)$

The derivative of f(x) is:

$\frac{d}{dx} [\log(x)] = \frac{1}{x}$

This shows that the derivative of a log function is always 1/x.

Successive Differentiation:

Successive differentiation is a technique used to find the derivative of a function that is composed of multiple functions. For example, consider the function:

$f(x) = x^2 \log(x)$

The derivative of f(x) is:

$\frac{d}{dx} [x^2 \log(x)] = \frac{2x \log(x)}{x}$

$= 2 \log(x)$

Successive differentiation can be used to find the derivatives of complex functions that are made up of multiple logarithmic functions

Logarithmic Differentiation:

Consider the function:

$f(x) = \log(x)$

The derivative of f(x) is:

$\frac{d}{dx} [\log(x)] = \frac{1}{x}$

This shows that the derivative of a log function is always 1/x.

Successive Differentiation:

Successive differentiation is a technique used to find the derivative of a function that is composed of multiple functions. For example, consider the function:

$f(x) = x^2 \log(x)$

The derivative of f(x) is:

$\frac{d}{dx} [x^2 \log(x)] = \frac{2x \log(x)}{x}$

$= 2 \log(x)$

Successive differentiation can be used to find the derivatives of complex functions that are made up of multiple logarithmic functions

Logarithmic differentiation and successive differentiation

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