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

Problem

d()/d(x)*(3*x3−2*x)* at *(1,1)

Solution

1. Identify the function to be differentiated, which is y=3*x3−2*x

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

3. Calculate the general derivative of the function.

d(y)/d(x)=3*(3*x2)−2*(1)

d(y)/d(x)=9*x2−2

4. Substitute the xcoordinate from the given point (1,1) into the derivative expression.

d(y)/d(x)|=9*(1)2−2

5. Simplify the result to find the slope at the specific point.

9−2=7

Final Answer

d()/d(x)*(3*x3−2*x)|=7

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