Find the Derivative - d/dx (x+8)(24/x+12)

Problem

d()/d(x)*(x+8)*(24/x+12)

Solution

1. Expand the expression using the FOIL method to simplify the differentiation process.

(x+8)*(24/x+12)=x*(24/x)+12*x+8*(24/x)+96

2. Simplify the terms within the expression.

24+12*x+192/x+96

3. Combine the constant terms.

12*x+192/x+120

4. Rewrite the fraction using a negative exponent to prepare for the power rule.

12*x+192*x(−1)+120

5. Apply the power rule to each term individually.

d()/d(x)*12*x=12

d()/d(x)*192*x(−1)=−192*x(−2)

d()/d(x)*120=0

6. Combine the results and rewrite the negative exponent as a fraction.

12−192/(x2)

Final Answer

d()/d(x)*(x+8)*(24/x+12)=12−192/(x2)

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