Find the Derivative - d/dx 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.

3. Differentiate the constant term 4 The derivative of any constant with respect to x is 0

4. Apply the power rule to the term −x2 The power rule states that d(xn)/d(x)=n*x(n−1)

5. Calculate the derivative of −x2 as −2*x(2−1) which simplifies to −2*x

6. Combine the results of the individual derivatives to find the final expression.

Final Answer

d(4−x2)/d(x)=−2*x

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