Find the Derivative - d/dx (4x-9)/(8x+1)

Problem

d()/d(x)(4*x−9)/(8*x+1)

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=4*x−9 and v=8*x+1

3. Differentiate both parts: d(u)/d(x)=4 and d(v)/d(x)=8

4. Substitute these values into the quotient rule formula:

((8*x+1)*(4)−(4*x−9)*(8))/((8*x+1)2)

5. Distribute the constants in the numerator:

(32*x+4−(32*x−72))/((8*x+1)2)

6. Simplify the numerator by combining like terms:

(32*x+4−32*x+72)/((8*x+1)2)

7. Combine the remaining constants:

76/((8*x+1)2)

Final Answer

d()/d(x)(4*x−9)/(8*x+1)=76/((8*x+1)2)

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