Find the Derivative - d/dx x-2y

Problem

d()/d(x)*(x−2*y)

Solution

1. Identify the type of differentiation required. Since the expression contains both x and y we use implicit differentiation, treating y as a function of x

2. Apply the sum rule for derivatives to differentiate each term separately.

d()/d(x)*(x−2*y)=d(x)/d(x)−(d(2)*y)/d(x)

3. Differentiate the first term with respect to x

d(x)/d(x)=1

4. Apply the chain rule to the second term. Since y is a function of x the derivative of 2*y is 2 multiplied by the derivative of y with respect to x

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

5. Combine the results to find the final expression for the derivative.

1−2d(y)/d(x)

Final Answer

d()/d(x)*(x−2*y)=1−2d(y)/d(x)

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