Find the Derivative - d/dx (x^2)/y

Problem

d()/d(x)(x2)/y

Solution

1. Identify the rule needed for differentiation. Since the expression is a quotient where y is an implicit function of x use the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Assign the variables for the quotient rule. Let u=x2 and v=y

3. Differentiate the numerator and denominator with respect to x

d(x2)/d(x)=2*x

d(y)/d(x)=d(y)/d(x)

4. Apply the quotient rule formula by substituting the derivatives back into the expression.

(y*(2*x)−x2d(y)/d(x))/(y2)

5. Simplify the numerator to reach the final form.

(2*x*y−x2d(y)/d(x))/(y2)

Final Answer

d()/d(x)(x2)/y=(2*x*y−x2d(y)/d(x))/(y2)

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