Math Problem Statement
Find the derivative of the algebraic function. f(x) = 7x − 3/√x
Solution
To find the derivative of the given algebraic function , let's go step-by-step.
1. Rewrite the function
We'll rewrite as a power of .
2. Differentiate term by term
Now, differentiate each term using basic differentiation rules:
- The derivative of is .
- The derivative of is found using the power rule .
3. Combine the derivatives
Thus, the derivative of the function is:
Final answer:
Would you like more details on any part of this process?
Here are some related questions:
- What is the power rule for differentiation?
- How do you differentiate terms with fractional exponents?
- How do we simplify negative exponents in derivatives?
- How can derivatives be used to find the slope of a curve?
- What does the derivative tell us about the behavior of a function?
Tip: Always rewrite terms with roots or fractions into exponents when differentiating—it makes the process easier!
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Math Problem Analysis
Mathematical Concepts
Algebra
Calculus
Differentiation
Power Rule
Formulas
Derivative of x^n: d/dx[x^n] = nx^(n-1)
Derivative of a constant multiple: d/dx[c*f(x)] = c * d/dx[f(x)]
Theorems
Power Rule
Constant Multiple Rule
Suitable Grade Level
Grades 11-12 (or early college level)