Solve (6.3x-5.4)+(5.4x-4.5)+(4.5x-3.6)+(3.6x-2.7)+(2.7x-1.8)+(1.8x-0.9)+0.9x

$$(6.3x-5.4)+(5.4x-4.5)+(4.5x-3.6)+(3.6x-2.7)+(2.7x-1.8)+(1.8x-0.9)+0.9x$$

Evaluate

$$\frac{126x}{5}-18.9$$

Solution Steps

Combine 6.3x and 5.4x to get 11.7x.

$$11.7x-5.4-4.5+4.5x-3.6+3.6x-2.7+2.7x-1.8+1.8x-0.9+0.9x$$

Subtract 4.5 from -5.4 to get -9.9.

$$11.7x-9.9+4.5x-3.6+3.6x-2.7+2.7x-1.8+1.8x-0.9+0.9x$$

Combine 11.7x and 4.5x to get 16.2x.

$$16.2x-9.9-3.6+3.6x-2.7+2.7x-1.8+1.8x-0.9+0.9x$$

Subtract 3.6 from -9.9 to get -13.5.

$$16.2x-13.5+3.6x-2.7+2.7x-1.8+1.8x-0.9+0.9x$$

Combine 16.2x and 3.6x to get 19.8x.

$$19.8x-13.5-2.7+2.7x-1.8+1.8x-0.9+0.9x$$

Subtract 2.7 from -13.5 to get -16.2.

$$19.8x-16.2+2.7x-1.8+1.8x-0.9+0.9x$$

Combine 19.8x and 2.7x to get 22.5x.

$$22.5x-16.2-1.8+1.8x-0.9+0.9x$$

Subtract 1.8 from -16.2 to get -18.

$$22.5x-18+1.8x-0.9+0.9x$$

Combine 22.5x and 1.8x to get 24.3x.

$$24.3x-18-0.9+0.9x$$

Subtract 0.9 from -18 to get -18.9.

$$24.3x-18.9+0.9x$$

Combine 24.3x and 0.9x to get 25.2x.

$$25.2x-18.9$$

Differentiate w.r.t. x

$$25.2$$

Steps Using Derivative Rule for Sum

Combine 6.3x and 5.4x to get 11.7x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11.7x-5.4-4.5+4.5x-3.6+3.6x-2.7+2.7x-1.8+1.8x-0.9+0.9x)$$

Subtract 4.5 from -5.4 to get -9.9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11.7x-9.9+4.5x-3.6+3.6x-2.7+2.7x-1.8+1.8x-0.9+0.9x)$$

Combine 11.7x and 4.5x to get 16.2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16.2x-9.9-3.6+3.6x-2.7+2.7x-1.8+1.8x-0.9+0.9x)$$

Subtract 3.6 from -9.9 to get -13.5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16.2x-13.5+3.6x-2.7+2.7x-1.8+1.8x-0.9+0.9x)$$

Combine 16.2x and 3.6x to get 19.8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(19.8x-13.5-2.7+2.7x-1.8+1.8x-0.9+0.9x)$$

Subtract 2.7 from -13.5 to get -16.2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(19.8x-16.2+2.7x-1.8+1.8x-0.9+0.9x)$$

Combine 19.8x and 2.7x to get 22.5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(22.5x-16.2-1.8+1.8x-0.9+0.9x)$$

Subtract 1.8 from -16.2 to get -18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(22.5x-18+1.8x-0.9+0.9x)$$

Combine 22.5x and 1.8x to get 24.3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24.3x-18-0.9+0.9x)$$

Subtract 0.9 from -18 to get -18.9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24.3x-18.9+0.9x)$$

Combine 24.3x and 0.9x to get 25.2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25.2x-18.9)$$

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}.

$$25.2x^{1-1}$$

Subtract 1 from 1.

$$25.2x^{0}$$

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

$$25.2\times 1$$

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

$$25.2$$