Solve (3x+1)+(x+1)+left(4x-3right)+left(3x-1right)

$$(3x+1)+(x+1)+ \left( 4x-3 \right) + \left( 3x-1 \right)$$

Evaluate

$$11x-2$$

Solution Steps

Combine 3x and x to get 4x.

$$4x+1+1+4x-3+3x-1$$

Add 1 and 1 to get 2.

$$4x+2+4x-3+3x-1$$

Combine 4x and 4x to get 8x.

$$8x+2-3+3x-1$$

Subtract 3 from 2 to get -1.

$$8x-1+3x-1$$

Combine 8x and 3x to get 11x.

$$11x-1-1$$

Subtract 1 from -1 to get -2.

$$11x-2$$

Differentiate w.r.t. x

$$11$$

Steps Using Derivative Rule for Sum

Combine 3x and x to get 4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x+1+1+4x-3+3x-1)$$

Add 1 and 1 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x+2+4x-3+3x-1)$$

Combine 4x and 4x to get 8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x+2-3+3x-1)$$

Subtract 3 from 2 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x-1+3x-1)$$

Combine 8x and 3x to get 11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x-1-1)$$

Subtract 1 from -1 to get -2.

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

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}.

$$11x^{1-1}$$

Subtract 1 from 1.

$$11x^{0}$$

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

$$11\times 1$$

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

$$11$$