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dy dx y = - 2x6 Find = 5 dx

dy dx y = - 2x6 Find = 5 dx

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question

 please show your derivative by hand and simplify

### Calculus: Differentiation Example **Problem:** Find \(\frac{dy}{dx}\). \[ y = -2x^6 \] --- **Solution:** To find the derivative \(\frac{dy}{dx}\), we apply the power rule to the expression: The power rule states that if \(y = ax^n\), then \(\frac{dy}{dx} = nax^{n-1}\). Applying the power rule to this expression: \[ y = -2x^6 \] \[ \frac{dy}{dx} = -2 \cdot 6x^{6-1} \] \[ \frac{dy}{dx} = -12x^5 \] However, the transcribed image indicates a final boxed solution as: \[ \frac{dy}{dx} = \boxed{5} \] Note: The final boxed solution appears incorrect based on the initially provided equation. Please verify the problem statement and calculation steps.
Transcribed Image Text:### Calculus: Differentiation Example **Problem:** Find \(\frac{dy}{dx}\). \[ y = -2x^6 \] --- **Solution:** To find the derivative \(\frac{dy}{dx}\), we apply the power rule to the expression: The power rule states that if \(y = ax^n\), then \(\frac{dy}{dx} = nax^{n-1}\). Applying the power rule to this expression: \[ y = -2x^6 \] \[ \frac{dy}{dx} = -2 \cdot 6x^{6-1} \] \[ \frac{dy}{dx} = -12x^5 \] However, the transcribed image indicates a final boxed solution as: \[ \frac{dy}{dx} = \boxed{5} \] Note: The final boxed solution appears incorrect based on the initially provided equation. Please verify the problem statement and calculation steps.
Expert Solution
Step 1: Rule of derivative

Given, y equals negative 2 x to the power of 6

we know fraction numerator d space over denominator d x end fraction left parenthesis x to the power of n right parenthesis equals n x to the power of n minus 1 end exponent


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