Solve x^2-2xx+2+2^2

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

Evaluate

$$6-x^{2}$$

Solution Steps

Multiply x and x to get x^{2}.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$-x^{2}+2+4$$

Add 2 and 4 to get 6.

$$-x^{2}+6$$

Differentiate w.r.t. x

$$-2x$$

Steps Using Derivative Rule for Sum

Multiply x and x to get x^{2}.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+2+4)$$

Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+6)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\left(-1\right)x^{2-1}$$

Multiply 2 times -1.

$$-2x^{2-1}$$

Subtract 1 from 2.

$$-2x^{1}$$

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

$$-2x$$