Logarithmic Differentiation

When we want to differentiate a function of the form f(x) g(x), we use logarithmic differentiation.When we want to differentiate a function of the form f(x) g(x), we use logarithmic differentiation.

Let y = f(x) g(x)

Taking log on both sides, we have logy = g(x) logf(x).

Differentiating with respect to x, we get,

Example:

Differentiate the function y = (sin x)^{cos x}.

Suggested answer:

y = (sin x)^{cos x}

Taking log on both sides, we have log y = cos x (log sin x)

Differentiating both sides with respect to x, we have