Math Problem Statement
d/dx cubert x
Solution
To differentiate (which is the cube root of ) with respect to , we can rewrite it as a power of .
Now, apply the power rule for differentiation, which states:
In this case, . So, we differentiate:
Thus, the derivative is:
Or equivalently:
Let me know if you'd like more details or have further questions!
Here are 5 follow-up questions for more exploration:
- How do you differentiate other roots, like square roots or higher-order roots of ?
- What would the derivative be if the function was ?
- How does the power rule work for fractional exponents?
- What is the integral of ?
- Can you apply the chain rule to differentiate a composite function like ?
Tip: To handle fractional exponents, remember that , which lets you treat roots as powers!
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Math Problem Analysis
Mathematical Concepts
Differentiation
Exponents
Power Rule
Formulas
d/dx(x^n) = n * x^(n-1)
x^(1/n) = nth root of x
Theorems
Power Rule for Differentiation
Suitable Grade Level
Grades 9-11