Solve (-1/2x)*(-2x^2)

$$( - \frac { 1 } { 2 } x ) \cdot ( - 2 x ^ { 2 } )$$

Evaluate

$$x^{3}$$

Solution Steps

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

$$-\frac{1}{2}x^{3}\left(-2\right)$$

Multiply -\frac{1}{2} and -2 to get 1.

$$x^{3}$$

Differentiate w.r.t. x

$$3x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{2}x^{3}\left(-2\right))$$

Multiply -\frac{1}{2} and -2 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3})$$

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

$$3x^{3-1}$$

Subtract 1 from 3.

$$3x^{2}$$