Solve -3x^2+9+7x-11-13x^2

$$- 3 x ^ { 2 } + 9 + 7 x - 11 - 13 x ^ { 2 }$$

Evaluate

$$-16x^{2}+7x-2$$

Solution Steps

Subtract 11 from 9 to get -2.

$$-3x^{2}-2+7x-13x^{2}$$

Combine -3x^{2} and -13x^{2} to get -16x^{2}.

$$-16x^{2}-2+7x$$

Differentiate w.r.t. x

$$7-32x$$

Steps Using Derivative Rule for Sum

Subtract 11 from 9 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{2}-2+7x-13x^{2})$$

Combine -3x^{2} and -13x^{2} to get -16x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-16x^{2}-2+7x)$$

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}.

$$2\left(-16\right)x^{2-1}+7x^{1-1}$$

Multiply 2 times -16.

$$-32x^{2-1}+7x^{1-1}$$

Subtract 1 from 2.

$$-32x^{1}+7x^{1-1}$$

Subtract 1 from 1.

$$-32x^{1}+7x^{0}$$

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

$$-32x+7x^{0}$$

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

$$-32x+7\times 1$$

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

$$-32x+7$$