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

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

Evaluate

$$-8x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-2x^{7}\times 4$$

Multiply -2 and 4 to get -8.

$$-8x^{7}$$

Differentiate w.r.t. x

$$-56x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{7}\times 4)$$

Multiply -2 and 4 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8x^{7})$$

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

$$7\left(-8\right)x^{7-1}$$

Multiply 7 times -8.

$$-56x^{7-1}$$

Subtract 1 from 7.

$$-56x^{6}$$