Mathematics: What’s the derivative of y = 1/(2x^5)?

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What’s the derivative of y = 1/(2x^5)? - id1257926226, Hellopeople233

Ответ:

dannaasc3282

03.02.2022

Mathematics

$\displaystyle y' = \frac{-5}{2x^6}$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = \frac{1}{2x^5}$

Step 2: Differentiate

Rewrite: $\displaystyle y = \frac{x^{-5}}{2}$ Derivative Property [Multiplied Constant]: $\displaystyle y' = \frac{1}{2} \frac{d}{dx}[x^{-5}]$ Basic Power Rule: $\displaystyle y' = \frac{1}{2}(-5x^{-6})$ Simplify: $\displaystyle y' = \frac{-5}{2x^6}$

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

Unit: Differentiation

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What’s the derivative of y = 1/(2x^5)?

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