Derivative of log base b of x
1/ x ln(b)
The derivative of log base b of x with respect to x can be found using the change of base formula and the chain rule.
Using the change of base formula, we can rewrite log base b of x as ln(x) divided by ln(b):
log_b(x) = ln(x) / ln(b)
Taking the derivative of both sides with respect to x yields:
d/dx (log_b(x)) = d/dx (ln(x) / ln(b))
Using the quotient rule of differentiation and the chain rule, we have:
d/dx (ln(x) / ln(b)) = [ln(b) d/dx (ln(x)) – ln(x) d/dx (ln(b))] / ln(b)^2
d/dx (ln(x)) = 1/x
d/dx (ln(b)) = 0
Substituting these values back into our equation and simplifying, we get:
d/dx (log_b(x)) = 1 / (x ln(b))
Therefore, the derivative of log base b of x with respect to x is 1 / (x ln(b)).
More Answers:
Left-Handed And Right-Handed Limits: Essential Concepts In CalculusHow To Verbalize Limit Functions In Math: Definition And Examples
Mastering The Ln(X) Power Formula: Learn The Simplified Process For Calculating R*Ln(X)
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded