Find the Derivative - d/dx (7x^2-9x+13)/(2x+4)

Problem

d()/d(x)(7*x2−9*x+13)/(2*x+4)

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 to u=7*x2−9*x+13 and the denominator to v=2*x+4

3. Differentiate the numerator to find d(u)/d(x)=14*x−9

4. Differentiate the denominator to find d(v)/d(x)=2

5. Substitute these components into the quotient rule formula.

d()/d(x)(7*x2−9*x+13)/(2*x+4)=((2*x+4)*(14*x−9)−(7*x2−9*x+13)*(2))/((2*x+4)2)

6. Expand the terms in the numerator.

(2*x+4)*(14*x−9)=28*x2−18*x+56*x−36=28*x2+38*x−36

(7*x2−9*x+13)*(2)=14*x2−18*x+26

7. Subtract the expanded terms in the numerator.

(28*x2+38*x−36)−(14*x2−18*x+26)=14*x2+56*x−62

8. Simplify the expression by factoring out a 2 from the numerator and the denominator.

(2*(7*x2+28*x−31))/((2*(x+2))2)=(2*(7*x2+28*x−31))/(4*(x+2)2)

(7*x2+28*x−31)/(2*(x+2)2)

Final Answer

d()/d(x)(7*x2−9*x+13)/(2*x+4)=(7*x2+28*x−31)/(2*(x+2)2)

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