Find the Derivative - d/d@VAR f(x)=4-x^2

Problem

d()/d(x)*(4−x2)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=4−x2

2. Apply the sum rule for derivatives, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

d(4−x2)/d(x)=d(4)/d(x)−d(x2)/d(x)

3. Differentiate the constant term. The derivative of any constant with respect to x is 0

d(4)/d(x)=0

4. Apply the power rule to the second term. For any term xn the derivative is n*x(n−1)

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

5. Combine the results to find the final derivative.

0−2*x=−2*x

Final Answer

d(4−x2)/d(x)=−2*x

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