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

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

Evaluate

$$-8x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

Multiply 2 and -4 to get -8.

$$-8x^{5}$$

Differentiate w.r.t. x

$$-40x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

Multiply 2 and -4 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8x^{5})$$

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

$$5\left(-8\right)x^{5-1}$$

Multiply 5 times -8.

$$-40x^{5-1}$$

Subtract 1 from 5.

$$-40x^{4}$$