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Differentiate Functions of Other Bases In Exercise, find the derivative of the function.

g(x) = log5 x

1 Answer

7 votes

Answer:

The derivative of the function is:


g'(x) = (1)/(1.6094x)

Explanation:

If we have a function in the following format:


g(x) = log_a(f(x))

This function has the following derivative


g'(x) = (f'(x))/(f(x)*ln(a))

In this problem, we have that:


g(x) = log_5(x)

So
f(x) = x, f'(x) = 1, a = 5

The derivative is


g'(x) = (f'(x))/(f(x)*ln(a))


g'(x) = (1)/(x*ln(5))


g'(x) = (1)/(1.6094x)

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