Solve x+2(-x)-3x-4x-5(6x)-3(4x)-9

$$x+2(-x)-3x-4x-5(6x)-3(4x)-9$$

Evaluate

$$-50x-9$$

Solution Steps

Combine x and -3x to get -2x.

$$-2x+2\left(-x\right)-4x-5\times 6x-3\times 4x-9$$

Combine -2x and -4x to get -6x.

$$-6x+2\left(-x\right)-5\times 6x-3\times 4x-9$$

Multiply 5 and 6 to get 30.

$$-6x+2\left(-x\right)-30x-3\times 4x-9$$

Combine -6x and -30x to get -36x.

$$-36x+2\left(-x\right)-3\times 4x-9$$

Multiply 3 and 4 to get 12.

$$-36x+2\left(-x\right)-12x-9$$

Combine -36x and -12x to get -48x.

$$-48x+2\left(-x\right)-9$$

Multiply 2 and -1 to get -2.

$$-48x-2x-9$$

Combine -48x and -2x to get -50x.

$$-50x-9$$

Differentiate w.r.t. x

$$-50$$

Steps Using Derivative Rule for Sum

Combine x and -3x to get -2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x+2\left(-x\right)-4x-5\times 6x-3\times 4x-9)$$

Combine -2x and -4x to get -6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x+2\left(-x\right)-5\times 6x-3\times 4x-9)$$

Multiply 5 and 6 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x+2\left(-x\right)-30x-3\times 4x-9)$$

Combine -6x and -30x to get -36x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-36x+2\left(-x\right)-3\times 4x-9)$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-36x+2\left(-x\right)-12x-9)$$

Combine -36x and -12x to get -48x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-48x+2\left(-x\right)-9)$$

Multiply 2 and -1 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-48x-2x-9)$$

Combine -48x and -2x to get -50x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-50x-9)$$

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}.

$$-50x^{1-1}$$

Subtract 1 from 1.

$$-50x^{0}$$

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

$$-50$$