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

Problem

d()/d(x)*(4−x2)

Solution

1. Identify the expression to be differentiated, which is a polynomial consisting of two terms: 4 and −x2

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

d(4−x2)/d(x)=d(4)/d(x)−d(x2)/d(x)

3. Apply the constant rule to the first term, noting that the derivative of any constant is 0

d(4)/d(x)=0

4. Apply the power rule to the second term, where d(xn)/d(x)=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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