Solve x^2-xy+y^2-x^2+xy+y^2

$$x ^ { 2 } - x y + y ^ { 2 } - x ^ { 2 } + x y + y ^ { 2 }$$

Evaluate

$$2y^{2}$$

Solution Steps

Combine x^{2} and -x^{2} to get 0.

$$-xy+y^{2}+xy+y^{2}$$

Combine -xy and xy to get 0.

$$y^{2}+y^{2}$$

Combine y^{2} and y^{2} to get 2y^{2}.

$$2y^{2}$$

Differentiate w.r.t. y

$$4y$$

Steps Using Definition of a Derivative

Combine x^{2} and -x^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-xy+y^{2}+xy+y^{2})$$

Combine -xy and xy to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{2}+y^{2})$$

Combine y^{2} and y^{2} to get 2y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y^{2})$$

The derivative of ax^{n} is nax^{n-1}.

$$2\times 2y^{2-1}$$

Multiply 2 times 2.

$$4y^{2-1}$$

Subtract 1 from 2.

$$4y^{1}$$

For any term t, t^{1}=t.

$$4y$$