Find the derivative of
\sqrt[3]{x} " alt=" y = \sqrt[3]{x} " align="absmiddle" class="latex-formula">
at the point where x = 27.
1 answer:
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Exponential Rule [Root Rewrite]:
- Exponential Rule [Rewrite]:
<u>Calculus</u>
Derivatives
Derivative Notation
Basic Power Rule
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
y = ∛x
x = 27
<u>Step 2: Differentiate</u>
- [Function] Rewrite [Exponential Rule - Root Rewrite]:
- Basic Power Rule:
- Simplify:
- Rewrite [Exponential Rule - Rewrite]:
<u>Step 3: Solve</u>
- Substitute<em> </em>in <em>x</em> [Derivative]:
- Evaluate exponents:
- Multiply:
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
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