Find the Derivative - d/d@VAR f(x)=1-x^2

Problem

d()/d(x)*(1−x^2)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=1−x^2

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 1 The derivative of any constant with respect to x is 0

4. Apply the power rule to the term −x^2 The power rule states that d(x^n)/d(x)=n*x^(n−1)

5. Simplify the resulting expression by combining the terms.

Final Answer

d(1−x^2)/d(x)=−2*x

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