Solve (5x+3x+6)+(7x-2x+3)=

$$( 5 x + 3 x + 6 ) + ( 7 x - 2 x + 3 ) =$$

Evaluate

$$13x+9$$

Solution Steps

Combine 5x and 3x to get 8x.

$$8x+6+7x-2x+3$$

Combine 8x and 7x to get 15x.

$$15x+6-2x+3$$

Combine 15x and -2x to get 13x.

$$13x+6+3$$

Add 6 and 3 to get 9.

$$13x+9$$

Differentiate w.r.t. x

$$13$$

Steps Using Derivative Rule for Sum

Combine 5x and 3x to get 8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x+6+7x-2x+3)$$

Combine 8x and 7x to get 15x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x+6-2x+3)$$

Combine 15x and -2x to get 13x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13x+6+3)$$

Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13x+9)$$

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}.

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

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.

$$13$$