Find the Derivative - d/dx (x^2-9)/(x-3)

Problem

d()/d(x)(x2−9)/(x−3)

Solution

1. Factor the numerator of the expression using the difference of squares formula, a2−b2=(a−b)*(a+b)

x2−9=(x−3)*(x+3)

2. Simplify the rational expression by canceling the common factor (x−3) from the numerator and the denominator, assuming x≠3

((x−3)*(x+3))/(x−3)=x+3

3. Apply the derivative to the simplified linear expression using the sum rule and the power rule.

d()/d(x)*(x+3)=d(x)/d(x)+d(3)/d(x)

4. Evaluate the derivatives of the individual terms.

d(x)/d(x)=1

d(3)/d(x)=0

Final Answer

d()/d(x)(x2−9)/(x−3)=1

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