Solve -11-10-9-8-7-6-5-4-3-2-101234567891011x

$$- 11 - 10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 101234567891011 x$$

Evaluate

$$-101234567891011x-65$$

Solution Steps

Subtract 10 from -11 to get -21.

$$-21-9-8-7-6-5-4-3-2-101234567891011x$$

Subtract 9 from -21 to get -30.

$$-30-8-7-6-5-4-3-2-101234567891011x$$

Subtract 8 from -30 to get -38.

$$-38-7-6-5-4-3-2-101234567891011x$$

Subtract 7 from -38 to get -45.

$$-45-6-5-4-3-2-101234567891011x$$

Subtract 6 from -45 to get -51.

$$-51-5-4-3-2-101234567891011x$$

Subtract 5 from -51 to get -56.

$$-56-4-3-2-101234567891011x$$

Subtract 4 from -56 to get -60.

$$-60-3-2-101234567891011x$$

Subtract 3 from -60 to get -63.

$$-63-2-101234567891011x$$

Subtract 2 from -63 to get -65.

$$-65-101234567891011x$$

Differentiate w.r.t. x

$$-101234567891011$$

Steps Using Derivative Rule for Sum

Subtract 10 from -11 to get -21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-21-9-8-7-6-5-4-3-2-101234567891011x)$$

Subtract 9 from -21 to get -30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-30-8-7-6-5-4-3-2-101234567891011x)$$

Subtract 8 from -30 to get -38.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-38-7-6-5-4-3-2-101234567891011x)$$

Subtract 7 from -38 to get -45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-45-6-5-4-3-2-101234567891011x)$$

Subtract 6 from -45 to get -51.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-51-5-4-3-2-101234567891011x)$$

Subtract 5 from -51 to get -56.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-56-4-3-2-101234567891011x)$$

Subtract 4 from -56 to get -60.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-60-3-2-101234567891011x)$$

Subtract 3 from -60 to get -63.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-63-2-101234567891011x)$$

Subtract 2 from -63 to get -65.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-65-101234567891011x)$$

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}.

$$-101234567891011x^{1-1}$$

Subtract 1 from 1.

$$-101234567891011x^{0}$$

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

$$-101234567891011$$