Solve 2x+1+3x-4+x+3

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

Evaluate

$$6x$$

Solution Steps

Combine 2x and 3x to get 5x.

$$5x+1-4+x+3$$

Subtract 4 from 1 to get -3.

$$5x-3+x+3$$

Combine 5x and x to get 6x.

$$6x-3+3$$

Add -3 and 3 to get 0.

$$6x$$

Differentiate w.r.t. x

$$6$$

Steps Using Definition of a Derivative

Combine 2x and 3x to get 5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x+1-4+x+3)$$

Subtract 4 from 1 to get -3.

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

Combine 5x and x to get 6x.

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

Add -3 and 3 to get 0.

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

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.

$$6$$