Math Problem Statement
Find the derivative of the function. f(x) = log5(x) f '(x) =
Solution
To find the derivative of , we can use the change of base formula for logarithms along with the derivative rules.
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Rewrite in terms of the natural logarithm:
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Differentiate with respect to :
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Use the derivative of , which is :
So, the derivative of is:
Would you like further clarification on any step?
Related Questions
- What is the derivative of for an arbitrary base ?
- How do we differentiate , where is a constant?
- What is the derivative of ?
- How would you find the second derivative of ?
- How is the change of base formula for logarithms useful in calculus?
Tip
When differentiating logarithmic functions with arbitrary bases, converting them to natural logarithms simplifies the process!
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Math Problem Analysis
Mathematical Concepts
Calculus
Logarithmic Differentiation
Formulas
Change of base formula: log_a(x) = ln(x)/ln(a)
Derivative of natural logarithm: d/dx(ln(x)) = 1/x
Theorems
Change of Base Formula
Derivative of Logarithmic Functions
Suitable Grade Level
Grades 11-12