Solve x^2+6x-4x^2-8x-12

$$x ^ { 2 } + 6 x - 4 x ^ { 2 } - 8 x - 12$$

Evaluate

$$-3x^{2}-2x-12$$

Solution Steps

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}+6x-8x-12$$

Combine 6x and -8x to get -2x.

$$-3x^{2}-2x-12$$

Differentiate w.r.t. x

$$-6x-2$$

Steps Using Derivative Rule for Sum

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{2}+6x-8x-12)$$

Combine 6x and -8x to get -2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{2}-2x-12)$$

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}.

$$2\left(-3\right)x^{2-1}-2x^{1-1}$$

Multiply 2 times -3.

$$-6x^{2-1}-2x^{1-1}$$

Subtract 1 from 2.

$$-6x^{1}-2x^{1-1}$$

Subtract 1 from 1.

$$-6x^{1}-2x^{0}$$

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

$$-6x-2x^{0}$$

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

$$-6x-2$$