Solve 5x+2+3x-1+5x+2

$$5 x + 2 + 3 x - 1 + 5 x + 2$$

Evaluate

$$13x+3$$

Solution Steps

Combine 5x and 3x to get 8x.

$$8x+2-1+5x+2$$

Subtract 1 from 2 to get 1.

$$8x+1+5x+2$$

Combine 8x and 5x to get 13x.

$$13x+1+2$$

Add 1 and 2 to get 3.

$$13x+3$$

Differentiate w.r.t. x

$$13$$

Steps Using Derivative Rule for Sum

Combine 5x and 3x to get 8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x+2-1+5x+2)$$

Subtract 1 from 2 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x+1+5x+2)$$

Combine 8x and 5x to get 13x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13x+1+2)$$

Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13x+3)$$

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}.

$$13x^{1-1}$$

Subtract 1 from 1.

$$13x^{0}$$

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

$$13\times 1$$

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

$$13$$