Friday, November 21, 2008

Logarithmic differentiation

To find derivatives of the functions of the form [f(x)]g(x)

Procedure is:
Let y = [f(x)]g(x)

Take logarithms on both sides

Log y = g(x)*log [f(x)]

Differentiate w.r.t. x
(1/y)*dy/dx = g(x)*(1/f(x))*d(f(x))/dx + log [f(x)]*d[g(x)]/dx

Therefore dy/dx = (1/y)*[ g(x)*(1/f(x))*d(f(x))/dx + log [f(x)]*d[g(x)]/dx]

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