Solve -4x^3*2x=

$$- 4 x ^ { 3 } \cdot 2 x =$$

Evaluate

$$-8x^{4}$$

Solution Steps

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

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

Multiply -4 and 2 to get -8.

$$-8x^{4}$$

Differentiate w.r.t. x

$$-32x^{3}$$

Steps Using Definition of a Derivative

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

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

Multiply -4 and 2 to get -8.

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

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

$$4\left(-8\right)x^{4-1}$$

Multiply 4 times -8.

$$-32x^{4-1}$$

Subtract 1 from 4.

$$-32x^{3}$$