Find the derivative of
at the point where x = 27.​

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Exponential Rule [Root Rewrite]: Exponential Rule [Rewrite]:

Calculus

Derivatives

Derivative Notation

Basic Power Rule

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

y = ∛x

x = 27

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]:                               Basic Power Rule:                                                                                         Simplify:                                                                                                         Rewrite [Exponential Rule - Rewrite]:                                                          

Step 3: Solve

Substitute in x [Derivative]:                                                                           Evaluate exponents:                                                                                     Multiply:                                                                                                        

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

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