Math Problem Statement
What is the derivative of 10^x with respect to x?
Solution
To solve the derivative of , we can use the general rule for differentiating exponential functions of the form , which is:
Here, . Therefore, the derivative of is:
So, the correct answer from the given options is D: .
Would you like more details on how to differentiate exponential functions or have any further questions?
Here are some related questions:
- How do you differentiate general exponential functions like ?
- What is the derivative of and how does it compare to ?
- Can you explain how logarithms come into play when differentiating exponentials?
- How would you apply the chain rule to derivatives of exponential functions like ?
- How can you differentiate expressions involving both exponents and logs, like ?
Tip: Remember that for bases other than , the natural logarithm appears in the derivative!
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Differentiation
Formulas
d/dx (a^x) = a^x * ln(a)
Theorems
Derivative of Exponential Functions
Suitable Grade Level
Grades 11-12