Find the Derivative Using Quotient Rule - d/dx (ax+b)/(cx+d)

Problem

d()/d(x)(a*x+b)/(c*x+d)

Solution

1. Identify the numerator and denominator functions for the quotient rule, where u=a*x+b and v=c*x+d

2. Differentiate the numerator and denominator with respect to x to find d(u)/d(x)=a and d(v)/d(x)=c

3. Apply the quotient rule formula, which states d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

4. Substitute the expressions into the formula:

((c*x+d)*(a)−(a*x+b)*(c))/((c*x+d)2)

5. Distribute the constants in the numerator:

(a*c*x+a*d−(a*c*x+b*c))/((c*x+d)2)

6. Simplify the numerator by subtracting the terms:

(a*c*x+a*d−a*c*x−b*c)/((c*x+d)2)

(a*d−b*c)/((c*x+d)2)

Final Answer

d()/d(x)(a*x+b)/(c*x+d)=(a*d−b*c)/((c*x+d)2)

Want more problems? Check here!