Solve x^3*(-2x)=

$$x ^ { 3 } \cdot ( - 2 x ) =$$

Differentiate w.r.t. x

$$-8x^{3}$$

Steps Using Definition of a Derivative

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

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

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

$$4\left(-2\right)x^{4-1}$$

Multiply 4 times -2.

$$-8x^{4-1}$$

Subtract 1 from 4.

$$-8x^{3}$$

Evaluate

$$-2x^{4}$$

Solution Steps

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

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