Solve 1-q-5-7q+8+8q-3q=

$$1 - q - 5 - 7 q + 8 + 8 q - 3 q =$$

Evaluate

$$4-3q$$

Solution Steps

Subtract 5 from 1 to get -4.

$$-4-q-7q+8+8q-3q$$

Combine -q and -7q to get -8q.

$$-4-8q+8+8q-3q$$

Add -4 and 8 to get 4.

$$4-8q+8q-3q$$

Combine -8q and 8q to get 0.

$$4-3q$$

Differentiate w.r.t. q

$$-3$$

Steps Using Derivative Rule for Sum

Subtract 5 from 1 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}q}(-4-q-7q+8+8q-3q)$$

Combine -q and -7q to get -8q.

$$\frac{\mathrm{d}}{\mathrm{d}q}(-4-8q+8+8q-3q)$$

Add -4 and 8 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}q}(4-8q+8q-3q)$$

Combine -8q and 8q to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}q}(4-3q)$$

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}.

$$-3q^{1-1}$$

Subtract 1 from 1.

$$-3q^{0}$$

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

$$-3$$