Solve (-7x-4y+6z)+(10x-20y-8z)+(-5x+24y+2z)

$$(-7x-4y+6z)+(10x-20y-8z)+(-5x+24y+2z)$$

Evaluate

$$-2x$$

Solution Steps

Combine -7x and 10x to get 3x.

$$3x-4y+6z-20y-8z-5x+24y+2z$$

Combine -4y and -20y to get -24y.

$$3x-24y+6z-8z-5x+24y+2z$$

Combine 6z and -8z to get -2z.

$$3x-24y-2z-5x+24y+2z$$

Combine 3x and -5x to get -2x.

$$-2x-24y-2z+24y+2z$$

Combine -24y and 24y to get 0.

$$-2x-2z+2z$$

Combine -2z and 2z to get 0.

$$-2x$$

Differentiate w.r.t. x

$$-2$$

Steps Using Definition of a Derivative

Combine -7x and 10x to get 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x-4y+6z-20y-8z-5x+24y+2z)$$

Combine -4y and -20y to get -24y.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x-24y+6z-8z-5x+24y+2z)$$

Combine 6z and -8z to get -2z.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x-24y-2z-5x+24y+2z)$$

Combine 3x and -5x to get -2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x-24y-2z+24y+2z)$$

Combine -24y and 24y to get 0.

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

Combine -2z and 2z to get 0.

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

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.

$$-2$$