Solve -3x^2+2+4x-16-8x^2

$$- 3 x ^ { 2 } + 2 + 4 x - 16 - 8 x ^ { 2 }$$

Evaluate

$$-11x^{2}+4x-14$$

Solution Steps

Subtract 16 from 2 to get -14.

$$-3x^{2}-14+4x-8x^{2}$$

Combine -3x^{2} and -8x^{2} to get -11x^{2}.

$$-11x^{2}-14+4x$$

Differentiate w.r.t. x

$$4-22x$$

Steps Using Derivative Rule for Sum

Subtract 16 from 2 to get -14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{2}-14+4x-8x^{2})$$

Combine -3x^{2} and -8x^{2} to get -11x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-11x^{2}-14+4x)$$

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}.

$$2\left(-11\right)x^{2-1}+4x^{1-1}$$

Multiply 2 times -11.

$$-22x^{2-1}+4x^{1-1}$$

Subtract 1 from 2.

$$-22x^{1}+4x^{1-1}$$

Subtract 1 from 1.

$$-22x^{1}+4x^{0}$$

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

$$-22x+4x^{0}$$

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

$$-22x+4\times 1$$

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

$$-22x+4$$