Solve (5q)(-16q)3

$$( 5 q ) ( - 16 q ) 3$$

Evaluate

$$-240q^{2}$$

Solution Steps

Multiply q and q to get q^{2}.

$$5q^{2}\left(-16\right)\times 3$$

Multiply 5 and -16 to get -80.

$$-80q^{2}\times 3$$

Multiply -80 and 3 to get -240.

$$-240q^{2}$$

Differentiate w.r.t. q

$$-480q$$

Steps Using Definition of a Derivative

Multiply q and q to get q^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}q}(5q^{2}\left(-16\right)\times 3)$$

Multiply 5 and -16 to get -80.

$$\frac{\mathrm{d}}{\mathrm{d}q}(-80q^{2}\times 3)$$

Multiply -80 and 3 to get -240.

$$\frac{\mathrm{d}}{\mathrm{d}q}(-240q^{2})$$

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

$$2\left(-240\right)q^{2-1}$$

Multiply 2 times -240.

$$-480q^{2-1}$$

Subtract 1 from 2.

$$-480q^{1}$$

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

$$-480q$$