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

Problem

d()/d(x)(x−4)/(x+4)

Solution

1. Identify the rule needed for the derivative of a quotient, which is the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Assign the numerator and denominator functions: u=x−4 and v=x+4

3. Differentiate the individual parts: d(x−4)/d(x)=1 and d(x+4)/d(x)=1

4. Substitute these values into the quotient rule formula:

((x+4)*(1)−(x−4)*(1))/((x+4)2)

5. Simplify the numerator by distributing and combining like terms:

(x+4−x+4)/((x+4)2)

6. Combine the constants in the numerator to reach the final simplified form:

8/((x+4)2)

Final Answer

d()/d(x)(x−4)/(x+4)=8/((x+4)2)

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