Solve x*x^2/2

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

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

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

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

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

Multiply 3 times \frac{1}{2}.

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

Subtract 1 from 3.

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

Evaluate

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

Solution Steps

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

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