Solve x^2-5x+8+x^2-4

$$x ^ { 2 } - 5 x + 8 + x ^ { 2 } - 4$$

Evaluate

$$2x^{2}-5x+4$$

Solution Steps

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

$$2x^{2}-5x+8-4$$

Subtract 4 from 8 to get 4.

$$2x^{2}-5x+4$$

Differentiate w.r.t. x

$$4x-5$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-5x+8-4)$$

Subtract 4 from 8 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-5x+4)$$

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}.

$$2\times 2x^{2-1}-5x^{1-1}$$

Multiply 2 times 2.

$$4x^{2-1}-5x^{1-1}$$

Subtract 1 from 2.

$$4x^{1}-5x^{1-1}$$

Subtract 1 from 1.

$$4x^{1}-5x^{0}$$

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

$$4x-5x^{0}$$

For any term t except 0, t^{0}=1.

$$4x-5$$