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

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

Evaluate

$$-24x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$2x^{3}\left(-3\right)\times 4x^{5}$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$2x^{8}\left(-3\right)\times 4$$

Multiply 2 and -3 to get -6.

$$-6x^{8}\times 4$$

Multiply -6 and 4 to get -24.

$$-24x^{8}$$

Differentiate w.r.t. x

$$-192x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}\left(-3\right)\times 4x^{5})$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{8}\left(-3\right)\times 4)$$

Multiply 2 and -3 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{8}\times 4)$$

Multiply -6 and 4 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-24x^{8})$$

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

$$8\left(-24\right)x^{8-1}$$

Multiply 8 times -24.

$$-192x^{8-1}$$

Subtract 1 from 8.

$$-192x^{7}$$