Solve (x+x+1*2x-5)+2x+4

$$(x+x+1 \times 2x-5)+2x+4$$

Evaluate

$$6x-1$$

Solution Steps

Combine x and x to get 2x.

$$2x+1\times 2x-5+2x+4$$

Multiply 1 and 2 to get 2.

$$2x+2x-5+2x+4$$

Combine 2x and 2x to get 4x.

$$4x-5+2x+4$$

Combine 4x and 2x to get 6x.

$$6x-5+4$$

Add -5 and 4 to get -1.

$$6x-1$$

Differentiate w.r.t. x

$$6$$

Steps Using Derivative Rule for Sum

Combine x and x to get 2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x+1\times 2x-5+2x+4)$$

Multiply 1 and 2 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x+2x-5+2x+4)$$

Combine 2x and 2x to get 4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x-5+2x+4)$$

Combine 4x and 2x to get 6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x-5+4)$$

Add -5 and 4 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x-1)$$

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}.

$$6x^{1-1}$$

Subtract 1 from 1.

$$6x^{0}$$

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

$$6\times 1$$

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

$$6$$