Solve (12x)(-2x^5)

$$( 12 x ) ( - 2 x ^ { 5 } )$$

Evaluate

$$-24x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$12x^{6}\left(-2\right)$$

Multiply 12 and -2 to get -24.

$$-24x^{6}$$

Differentiate w.r.t. x

$$-144x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{6}\left(-2\right))$$

Multiply 12 and -2 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-24x^{6})$$

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

$$6\left(-24\right)x^{6-1}$$

Multiply 6 times -24.

$$-144x^{6-1}$$

Subtract 1 from 6.

$$-144x^{5}$$