Solve (-2x^3)(5x)(-8x^4)

$$( - 2 x ^ { 3 } ) ( 5 x ) ( - 8 x ^ { 4 } )$$

Evaluate

$$80x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-2x^{4}\times 5\left(-8\right)x^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$-2x^{8}\times 5\left(-8\right)$$

Multiply -2 and 5 to get -10.

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

Multiply -10 and -8 to get 80.

$$80x^{8}$$

Differentiate w.r.t. x

$$640x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{4}\times 5\left(-8\right)x^{4})$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{8}\times 5\left(-8\right))$$

Multiply -2 and 5 to get -10.

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

Multiply -10 and -8 to get 80.

$$\frac{\mathrm{d}}{\mathrm{d}x}(80x^{8})$$

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

$$8\times 80x^{8-1}$$

Multiply 8 times 80.

$$640x^{8-1}$$

Subtract 1 from 8.

$$640x^{7}$$