Find the Derivative - d/dx (2x+5)/(3x-2)

Problem

d()/d(x)(2*x+5)/(3*x−2)

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=2*x+5 and v=3*x−2

3. Differentiate the individual components: d(2*x+5)/d(x)=2 and d(3*x−2)/d(x)=3

4. Substitute these values into the quotient rule formula:

((3*x−2)*(2)−(2*x+5)*(3))/((3*x−2)2)

5. Distribute the constants in the numerator:

(6*x−4−(6*x+15))/((3*x−2)2)

6. Simplify the numerator by combining like terms:

(6*x−4−6*x−15)/((3*x−2)2)

(−19)/((3*x−2)2)

Final Answer

d()/d(x)(2*x+5)/(3*x−2)=−19/((3*x−2)2)

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