Solve 41-10-9-8-7-6-5-4-3-2-10-1234567891011x

$$41 - 10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 10 - 1234567891011 x$$

Evaluate

$$-1234567891011x-23$$

Solution Steps

Subtract 10 from 41 to get 31.

$$31-9-8-7-6-5-4-3-2-10-1234567891011x$$

Subtract 9 from 31 to get 22.

$$22-8-7-6-5-4-3-2-10-1234567891011x$$

Subtract 8 from 22 to get 14.

$$14-7-6-5-4-3-2-10-1234567891011x$$

Subtract 7 from 14 to get 7.

$$7-6-5-4-3-2-10-1234567891011x$$

Subtract 6 from 7 to get 1.

$$1-5-4-3-2-10-1234567891011x$$

Subtract 5 from 1 to get -4.

$$-4-4-3-2-10-1234567891011x$$

Subtract 4 from -4 to get -8.

$$-8-3-2-10-1234567891011x$$

Subtract 3 from -8 to get -11.

$$-11-2-10-1234567891011x$$

Subtract 2 from -11 to get -13.

$$-13-10-1234567891011x$$

Subtract 10 from -13 to get -23.

$$-23-1234567891011x$$

Differentiate w.r.t. x

$$-1234567891011$$

Steps Using Derivative Rule for Sum

Subtract 10 from 41 to get 31.

$$\frac{\mathrm{d}}{\mathrm{d}x}(31-9-8-7-6-5-4-3-2-10-1234567891011x)$$

Subtract 9 from 31 to get 22.

$$\frac{\mathrm{d}}{\mathrm{d}x}(22-8-7-6-5-4-3-2-10-1234567891011x)$$

Subtract 8 from 22 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(14-7-6-5-4-3-2-10-1234567891011x)$$

Subtract 7 from 14 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7-6-5-4-3-2-10-1234567891011x)$$

Subtract 6 from 7 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1-5-4-3-2-10-1234567891011x)$$

Subtract 5 from 1 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4-4-3-2-10-1234567891011x)$$

Subtract 4 from -4 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8-3-2-10-1234567891011x)$$

Subtract 3 from -8 to get -11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-11-2-10-1234567891011x)$$

Subtract 2 from -11 to get -13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-13-10-1234567891011x)$$

Subtract 10 from -13 to get -23.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-23-1234567891011x)$$

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}.

$$-1234567891011x^{1-1}$$

Subtract 1 from 1.

$$-1234567891011x^{0}$$

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

$$-1234567891011$$