Solve (4x-5y+3z)+(-4x+5y+3z)

$$( 4 x - 5 y + 3 z ) + ( - 4 x + 5 y + 3 z )$$

Evaluate

$$6z$$

Solution Steps

Combine 4x and -4x to get 0.

$$-5y+3z+5y+3z$$

Combine -5y and 5y to get 0.

$$3z+3z$$

Combine 3z and 3z to get 6z.

$$6z$$

Differentiate w.r.t. z

$$6$$

Steps Using Definition of a Derivative

Combine 4x and -4x to get 0.

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

Combine -5y and 5y to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}z}(3z+3z)$$

Combine 3z and 3z to get 6z.

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

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

$$6z^{1-1}$$

Subtract 1 from 1.

$$6z^{0}$$

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

$$6\times 1$$

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

$$6$$