Evaluate the Derivative at @POINT y=2x^3-5x , (1,-3)

Problem

d()/d(x)*(2*x^3−5*x)* at *(1,−3)

Solution

1. Identify the function to be differentiated, which is y=2*x^3−5*x

2. Apply the power rule to each term of the expression, where d(x^n)/d(x)=n*x^(n−1)

3. Calculate the derivative of the first term: (d(2)*x^3)/d(x)=6*x^2

4. Calculate the derivative of the second term: (d(5)*x)/d(x)=5

5. Combine the results to find the general derivative expression d(y)/d(x)=6*x^2−5

6. Substitute the xcoordinate of the given point (1,−3) into the derivative expression.

7. Evaluate the numerical result: 6*(1)^2−5=6−5=1

Final Answer

d(2*x^3−5*x)/d(x)|=1

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