Evaluate the Derivative at @POINT y=x^3-2x , (2,4)

Problem

(d(x3)−2*x)/d(x)* at *(2,4)

Solution

1. Identify the function to be differentiated, which is y=x3−2*x

2. Apply the power rule to each term of the expression. The power rule states d(xn)/d(x)=n*x(n−1)

3. Calculate the derivative of the first term: d(x3)/d(x)=3*x2

4. Calculate the derivative of the second term: (d(2)*x)/d(x)=2

5. Combine the results to find the general derivative expression: d(y)/d(x)=3*x2−2

6. Substitute the xcoordinate from the given point (2,4) into the derivative expression.

7. Evaluate the numerical result: 3*(2)2−2=3*(4)−2=12−2=10

Final Answer

(d(x3)−2*x)/d(x)|=10

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