Find the Derivative - d/dx x^3-9x

Problem

d()/d(x)*(x3−9*x)

Solution

1. Identify the expression as a difference of two terms, allowing the use of the sum/difference rule for derivatives.

2. Apply the power rule to the first term, x3 which states that d(xn)/d(x)=n*x(n−1)

3. Differentiate the first term.

d(x3)/d(x)=3*x2

4. Apply the constant multiple rule and the power rule to the second term, −9*x

5. Differentiate the second term.

(d(9)*x)/d(x)=9

6. Combine the results to find the final derivative.

Final Answer

(d(x3)−9*x)/d(x)=3*x2−9

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