Find the Derivative - d/dy x^2+xy+y^2

Problem

d()/d(y)*(x^2+x*y+y^2)

Solution

1. Identify the variable of differentiation, which is y This means x is treated as a constant.

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

3. Differentiate the first term x^2 Since x is a constant relative to y its derivative is zero.

d(x^2)/d(y)=0

4. Differentiate the second term x*y Since x is a constant coefficient, pull it out and differentiate y

(d(x)*y)/d(y)=x⋅d(y)/d(y)=x⋅1=x

5. Differentiate the third term y^2 using the power rule.

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

6. Combine the results of the individual derivatives to find the final expression.

Final Answer

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

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