Solve 4+7z+3-2z

$$4 + 7 z + 3 - 2 z$$

Evaluate

$$5z+7$$

Solution Steps

Add 4 and 3 to get 7.

$$7+7z-2z$$

Combine 7z and -2z to get 5z.

$$7+5z$$

Differentiate w.r.t. z

$$5$$

Steps Using Derivative Rule for Sum

Add 4 and 3 to get 7.

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

Combine 7z and -2z to get 5z.

$$\frac{\mathrm{d}}{\mathrm{d}z}(7+5z)$$

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}.

$$5z^{1-1}$$

Subtract 1 from 1.

$$5z^{0}$$

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

$$5\times 1$$

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

$$5$$