Find the Derivative - d/dx 24/(x^2+12)

Problem

d()/d(x)24/(x2+12)

Solution

1. Identify the expression as a constant divided by a function, which can be rewritten using a negative exponent to avoid the quotient rule: 24*(x2+12)(−1)

2. Apply the chain rule by taking the derivative of the outer function (the power) and multiplying it by the derivative of the inner function (x2+12.

3. Differentiate the outer function: −24*(x2+12)(−2)

4. Differentiate the inner function: (d(x2)+12)/d(x)=2*x

5. Multiply the results together: −24*(x2+12)(−2)⋅2*x

6. Simplify the expression by multiplying the constants and variables in the numerator and moving the negative exponent to the denominator.

Final Answer

d()/d(x)24/(x2+12)=−(48*x)/((x2+12)2)

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