Solve x^2+7x+2-2x^2-3x-7

$$x ^ { 2 } + 7 x + 2 - 2 x ^ { 2 } - 3 x - 7$$

Evaluate

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

Solution Steps

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

$$-x^{2}+7x+2-3x-7$$

Combine 7x and -3x to get 4x.

$$-x^{2}+4x+2-7$$

Subtract 7 from 2 to get -5.

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

Differentiate w.r.t. x

$$4-2x$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+7x+2-3x-7)$$

Combine 7x and -3x to get 4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+4x+2-7)$$

Subtract 7 from 2 to get -5.

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

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}.

$$2\left(-1\right)x^{2-1}+4x^{1-1}$$

Multiply 2 times -1.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$-2x^{1}+4x^{0}$$

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

$$-2x+4x^{0}$$

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

$$-2x+4\times 1$$

For any term t, t\times 1=t and 1t=t.

$$-2x+4$$