Find the Derivative - d/dx 4-x^2

Problem

d()/d(x)*(4−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)*(4−x2)=d(4)/d(x)−d(x2)/d(x)

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

d(4)/d(x)=0

3. Apply the power rule to the second term, where d(xn)/d(x)=n*x(n−1)

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

4. Combine the results to find the final derivative.

0−2*x=−2*x

Final Answer

d()/d(x)*(4−x2)=−2*x

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