Solve -2x+2+-1*0.1+0*0.1+1*0.4+2*0.2

$$- 2 x + 2 + - 1 \times 0.1 + 0 \times 0.1 + 1 \times 0.4 + 2 \times 0.2$$

Evaluate

$$2.7-2x$$

Solution Steps

Multiply -1 and 0.1 to get -0.1.

$$-2x+2-0.1+0\times 0.1+1\times 0.4+2\times 0.2$$

Subtract 0.1 from 2 to get 1.9.

$$-2x+1.9+0\times 0.1+1\times 0.4+2\times 0.2$$

Multiply 0 and 0.1 to get 0.

$$-2x+1.9+0+1\times 0.4+2\times 0.2$$

Add 1.9 and 0 to get 1.9.

$$-2x+1.9+1\times 0.4+2\times 0.2$$

Multiply 1 and 0.4 to get 0.4.

$$-2x+1.9+0.4+2\times 0.2$$

Add 1.9 and 0.4 to get 2.3.

$$-2x+2.3+2\times 0.2$$

Multiply 2 and 0.2 to get 0.4.

$$-2x+2.3+0.4$$

Add 2.3 and 0.4 to get 2.7.

$$-2x+2.7$$

Differentiate w.r.t. x

$$-2$$

Steps Using Derivative Rule for Sum

Multiply -1 and 0.1 to get -0.1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x+2-0.1+0\times 0.1+1\times 0.4+2\times 0.2)$$

Subtract 0.1 from 2 to get 1.9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x+1.9+0\times 0.1+1\times 0.4+2\times 0.2)$$

Multiply 0 and 0.1 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x+1.9+0+1\times 0.4+2\times 0.2)$$

Add 1.9 and 0 to get 1.9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x+1.9+1\times 0.4+2\times 0.2)$$

Multiply 1 and 0.4 to get 0.4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x+1.9+0.4+2\times 0.2)$$

Add 1.9 and 0.4 to get 2.3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x+2.3+2\times 0.2)$$

Multiply 2 and 0.2 to get 0.4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x+2.3+0.4)$$

Add 2.3 and 0.4 to get 2.7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x+2.7)$$

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}.

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

Subtract 1 from 1.

$$-2x^{0}$$

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

$$-2$$