Solve 3q+4q+7q-4q+4q-q

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

Evaluate

$$13q$$

Solution Steps

Combine 3q and 4q to get 7q.

$$7q+7q-4q+4q-q$$

Combine 7q and 7q to get 14q.

$$14q-4q+4q-q$$

Combine 14q and -4q to get 10q.

$$10q+4q-q$$

Combine 10q and 4q to get 14q.

$$14q-q$$

Combine 14q and -q to get 13q.

$$13q$$

Differentiate w.r.t. q

$$13$$

Steps Using Definition of a Derivative

Combine 3q and 4q to get 7q.

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

Combine 7q and 7q to get 14q.

$$\frac{\mathrm{d}}{\mathrm{d}q}(14q-4q+4q-q)$$

Combine 14q and -4q to get 10q.

$$\frac{\mathrm{d}}{\mathrm{d}q}(10q+4q-q)$$

Combine 10q and 4q to get 14q.

$$\frac{\mathrm{d}}{\mathrm{d}q}(14q-q)$$

Combine 14q and -q to get 13q.

$$\frac{\mathrm{d}}{\mathrm{d}q}(13q)$$

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

$$13q^{1-1}$$

Subtract 1 from 1.

$$13q^{0}$$

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

$$13\times 1$$

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

$$13$$