Find the Derivative - d/dx 8/(x^2+4)

Problem

d()/d(x)8/(x2+4)

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: 8*(x2+4)(−1)

2. Apply the power rule and the chain rule by bringing the exponent down and multiplying by the derivative of the inner function x2+4

3. Differentiate the inner function x2+4 to get 2*x

4. Multiply the terms together: 8⋅(−1)⋅(x2+4)(−2)⋅2*x

5. Simplify the expression by combining the constants and moving the negative exponent back to the denominator.

Final Answer

d()/d(x)8/(x2+4)=−(16*x)/((x2+4)2)

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