Solve -x+(-11x)+(+19x)+(-7x)+(+2x)

$$- x + ( - 11 x ) + ( + 19 x ) + ( - 7 x ) + ( + 2 x )$$

Evaluate

$$2x$$

Solution Steps

Combine -11x and 19x to get 8x.

$$-x+8x-7x+2x$$

Combine 8x and -7x to get x.

$$-x+x+2x$$

Combine x and 2x to get 3x.

$$-x+3x$$

Combine -x and 3x to get 2x.

$$2x$$

Differentiate w.r.t. x

$$2$$

Steps Using Definition of a Derivative

Combine -11x and 19x to get 8x.

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

Combine 8x and -7x to get x.

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

Combine x and 2x to get 3x.

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

Combine -x and 3x to get 2x.

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

The derivative of ax^{n} is nax^{n-1}.

$$2x^{1-1}$$

Subtract 1 from 1.

$$2x^{0}$$

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

$$2\times 1$$

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

$$2$$