Math Problem Statement
Derivate
Solution
To find the derivative of the function:
we'll differentiate each term separately.
Step 1: Differentiate
To differentiate , we use the general formula for the derivative of an exponential function with a base other than : where and , so .
Thus,
Step 2: Differentiate
To differentiate , we apply the chain rule:
Step 3: Combine the Results
Now, combining both derivatives, we have:
Final Answer
Would you like further details on any step, or do you have any questions?
Related Questions
- How do we apply the chain rule in more complex functions?
- What is the derivative of where ?
- How would the result change if the function were instead?
- How can we integrate and ?
- What if we wanted to find the second derivative of this function?
Tip
For exponential functions with bases other than , remember to multiply by after differentiating the exponent.
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Exponential Functions
Formulas
Derivative of a^u: d/dx (a^u) = a^u * ln(a) * u'
Derivative of e^u: d/dx (e^u) = e^u * u'
Theorems
Chain Rule
Suitable Grade Level
Grades 11-12