Solve x+x+x+x+x+x+x+x+3

$$x+x+x+x+x+x+x+x+3$$

Evaluate

$$8x+3$$

Solution Steps

Combine x and x to get 2x.

$$2x+x+x+x+x+x+x+3$$

Combine 2x and x to get 3x.

$$3x+x+x+x+x+x+3$$

Combine 3x and x to get 4x.

$$4x+x+x+x+x+3$$

Combine 4x and x to get 5x.

$$5x+x+x+x+3$$

Combine 5x and x to get 6x.

$$6x+x+x+3$$

Combine 6x and x to get 7x.

$$7x+x+3$$

Combine 7x and x to get 8x.

$$8x+3$$

Differentiate w.r.t. x

$$8$$

Steps Using Derivative Rule for Sum

Combine x and x to get 2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x+x+x+x+x+x+x+3)$$

Combine 2x and x to get 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+x+x+x+x+x+3)$$

Combine 3x and x to get 4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x+x+x+x+x+3)$$

Combine 4x and x to get 5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x+x+x+x+3)$$

Combine 5x and x to get 6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x+x+x+3)$$

Combine 6x and x to get 7x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x+x+3)$$

Combine 7x and x to get 8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x+3)$$

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}.

$$8x^{1-1}$$

Subtract 1 from 1.

$$8x^{0}$$

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

$$8\times 1$$

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

$$8$$