Find the Derivative - d/dx 9-x^2

Problem

d()/d(x)*(9−x2)

Solution

1. Apply the sum/difference rule of differentiation, which allows for the derivative of each term to be taken separately.

d()/d(x)*(9−x2)=d(9)/d(x)−d(x2)/d(x)

2. Differentiate the constant term using the rule that the derivative of any constant is zero.

d(9)/d(x)=0

3. Differentiate the power term using the power rule, which states that d(xn)/d(x)=n*x(n−1)

d(x2)/d(x)=2*x

4. Combine the results to find the final derivative of the expression.

0−2*x=−2*x

Final Answer

d()/d(x)*(9−x2)=−2*x

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