Solve 4x^2*(-1/2x)

$$4 x ^ { 2 } \times ( - \frac { 1 } { 2 } x )$$

Evaluate

$$-2x^{3}$$

Solution Steps

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

$$4x^{3}\left(-\frac{1}{2}\right)$$

Multiply 4 and -\frac{1}{2} to get -2.

$$-2x^{3}$$

Differentiate w.r.t. x

$$-6x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}\left(-\frac{1}{2}\right))$$

Multiply 4 and -\frac{1}{2} to get -2.

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

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

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

Multiply 3 times -2.

$$-6x^{3-1}$$

Subtract 1 from 3.

$$-6x^{2}$$