Solve (2x)+(x-5)+(2x-30)+(6x+3)+(2x-2)

$$( 2 x ) + ( x - 5 ) + ( 2 x - 30 ) + ( 6 x + 3 ) + ( 2 x - 2 )$$

Evaluate

$$13x-34$$

Solution Steps

Combine 2x and x to get 3x.

$$3x-5+2x-30+6x+3+2x-2$$

Combine 3x and 2x to get 5x.

$$5x-5-30+6x+3+2x-2$$

Subtract 30 from -5 to get -35.

$$5x-35+6x+3+2x-2$$

Combine 5x and 6x to get 11x.

$$11x-35+3+2x-2$$

Add -35 and 3 to get -32.

$$11x-32+2x-2$$

Combine 11x and 2x to get 13x.

$$13x-32-2$$

Subtract 2 from -32 to get -34.

$$13x-34$$

Differentiate w.r.t. x

$$13$$

Steps Using Derivative Rule for Sum

Combine 2x and x to get 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x-5+2x-30+6x+3+2x-2)$$

Combine 3x and 2x to get 5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x-5-30+6x+3+2x-2)$$

Subtract 30 from -5 to get -35.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x-35+6x+3+2x-2)$$

Combine 5x and 6x to get 11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x-35+3+2x-2)$$

Add -35 and 3 to get -32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x-32+2x-2)$$

Combine 11x and 2x to get 13x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13x-32-2)$$

Subtract 2 from -32 to get -34.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13x-34)$$

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.

$$13$$