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

Problem

d()/d(x)x/(x−4)

Solution

1. Identify the rule needed for the derivative of a quotient of two functions, which is the quotient rule.

2. Apply the formula for the quotient rule, d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2) where u=x and v=x−4

3. Differentiate the numerator and denominator separately, where d(x)/d(x)=1 and d(x−4)/d(x)=1

4. Substitute these derivatives back into the quotient rule formula.

d()/d(x)x/(x−4)=((x−4)*(1)−(x)*(1))/((x−4)2)

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

(x−4−x)/((x−4)2)

6. Finalize the expression by canceling the x terms in the numerator.

(−4)/((x−4)2)

Final Answer

d()/d(x)x/(x−4)=−4/((x−4)2)

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