Solve (2x^8)(-8x^2)(2x^3)

$$( 2 x ^ { 8 } ) ( - 8 x ^ { 2 } ) ( 2 x ^ { 3 } )$$

Evaluate

$$-32x^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$2x^{10}\left(-8\right)\times 2x^{3}$$

To multiply powers of the same base, add their exponents. Add 10 and 3 to get 13.

$$2x^{13}\left(-8\right)\times 2$$

Multiply 2 and -8 to get -16.

$$-16x^{13}\times 2$$

Multiply -16 and 2 to get -32.

$$-32x^{13}$$

Differentiate w.r.t. x

$$-416x^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{10}\left(-8\right)\times 2x^{3})$$

To multiply powers of the same base, add their exponents. Add 10 and 3 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{13}\left(-8\right)\times 2)$$

Multiply 2 and -8 to get -16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-16x^{13}\times 2)$$

Multiply -16 and 2 to get -32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-32x^{13})$$

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

$$13\left(-32\right)x^{13-1}$$

Multiply 13 times -32.

$$-416x^{13-1}$$

Subtract 1 from 13.

$$-416x^{12}$$