Find dy/dx y=(x^2)/(3x-1)

Problem

d()/d(x)(x2)/(3*x−1)

Solution

1. Identify the rule needed for differentiation. Since the function is a quotient of two expressions, use the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Assign the numerator and denominator to variables. Let u=x2 and v=3*x−1

3. Differentiate each part with respect to x

d(u)/d(x)=2*x

d(v)/d(x)=3

4. Substitute these components into the quotient rule formula.

d(y)/d(x)=((3*x−1)*(2*x)−(x2)*(3))/((3*x−1)2)

5. Expand the terms in the numerator.

d(y)/d(x)=(6*x2−2*x−3*x2)/((3*x−1)2)

6. Combine like terms to simplify the numerator.

d(y)/d(x)=(3*x2−2*x)/((3*x−1)2)

Final Answer

d(y)/d(x)=(3*x2−2*x)/((3*x−1)2)

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