Solve 1/2x*2/3x^2

$$\frac { 1 } { 2 } x \cdot \frac { 2 } { 3 } x ^ { 2 }$$

Evaluate

$$\frac{x^{3}}{3}$$

Solution Steps

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

$$\frac{1}{2}x^{3}\times \frac{2}{3}$$

Multiply \frac{1}{2} and \frac{2}{3} to get \frac{1}{3}.

$$\frac{1}{3}x^{3}$$

Differentiate w.r.t. x

$$x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{3}\times \frac{2}{3})$$

Multiply \frac{1}{2} and \frac{2}{3} to get \frac{1}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3}x^{3})$$

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

$$3\times \frac{1}{3}x^{3-1}$$

Multiply 3 times \frac{1}{3}.

$$x^{3-1}$$

Subtract 1 from 3.

$$x^{2}$$