Solve 3x^2+2x-7-5x-9x^2+2x-12

$$3 x ^ { 2 } + 2 x - 7 - 5 x - 9 x ^ { 2 } + 2 x - 12$$

Evaluate

$$-6x^{2}-x-19$$

Solution Steps

Combine 2x and -5x to get -3x.

$$3x^{2}-3x-7-9x^{2}+2x-12$$

Combine 3x^{2} and -9x^{2} to get -6x^{2}.

$$-6x^{2}-3x-7+2x-12$$

Combine -3x and 2x to get -x.

$$-6x^{2}-x-7-12$$

Subtract 12 from -7 to get -19.

$$-6x^{2}-x-19$$

Differentiate w.r.t. x

$$-12x-1$$

Steps Using Derivative Rule for Sum

Combine 2x and -5x to get -3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}-3x-7-9x^{2}+2x-12)$$

Combine 3x^{2} and -9x^{2} to get -6x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{2}-3x-7+2x-12)$$

Combine -3x and 2x to get -x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{2}-x-7-12)$$

Subtract 12 from -7 to get -19.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{2}-x-19)$$

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}.

$$2\left(-6\right)x^{2-1}-x^{1-1}$$

Multiply 2 times -6.

$$-12x^{2-1}-x^{1-1}$$

Subtract 1 from 2.

$$-12x^{1}-x^{1-1}$$

Subtract 1 from 1.

$$-12x^{1}-x^{0}$$

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

$$-12x-x^{0}$$

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

$$-12x-1$$