Derivative of log base b of x
1/ x ln(b)
The derivative of log base b of x can be found using the chain rule of differentiation.
Let y = logb(x), then we can rewrite y in terms of natural logarithm using the change of base formula:
y = logb(x) = ln(x) / ln(b)
Now, taking the derivative with respect to x:
dy/dx = d/dx[ln(x) / ln(b)]
Using the quotient rule of differentiation, we get:
dy/dx = [(1/x) * ln(b) – (ln(x) * 0)] / (ln(b))^2
Simplifying the expression, we get:
dy/dx = (1 / (x * ln(b)))
Therefore, the derivative of log base b of x is (1 / (x * ln(b))).
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