Find the Derivative - d/dx y=1/(1+x^2)

Problem

d()/d(x)1/(1+x2)

Solution

1. Identify the function as a reciprocal or a composition of functions, which can be solved using the Power Rule combined with the Chain Rule by rewriting the expression.

2. Rewrite the expression using a negative exponent to avoid the Quotient Rule.

y=(1+x2)(−1)

3. Apply the Power Rule by bringing the exponent down and subtracting one from the exponent.

d(y)/d(x)=−1*(1+x2)(−2)⋅d(1+x2)/d(x)

4. Apply the Chain Rule by multiplying by the derivative of the inner function 1+x2

d(1+x2)/d(x)=2*x

5. Substitute the inner derivative back into the expression.

d(y)/d(x)=−1*(1+x2)(−2)⋅2*x

6. Simplify the expression by moving the negative exponent back to the denominator.

d(y)/d(x)=(−2*x)/((1+x2)2)

Final Answer

d()/d(x)1/(1+x2)=−(2*x)/((1+x2)2)

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