Find the Derivative - d/dx 1-x^2

Problem

d()/d(x)*(1−x2)

Solution

1. Apply the sum/difference rule of differentiation, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

d()/d(x)*(1−x2)=d(1)/d(x)−d(x2)/d(x)

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

d(1)/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.

0−2*x=−2*x

Final Answer

d()/d(x)*(1−x2)=−2*x

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