Solve x^2/6*3/2x

$$\frac { x ^ { 2 } } { 6 } \cdot \frac { 3 } { 2 x }$$

Evaluate

$$\frac{x}{4}$$

Solution Steps

Multiply \frac{x^{2}}{6} times \frac{3}{2x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}\times 3}{6\times 2x}$$

Cancel out 3x in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

$$\frac{x}{4}$$

Differentiate w.r.t. x

$$\frac{1}{4} = 0.25$$

Steps Using Definition of a Derivative

Multiply \frac{x^{2}}{6} times \frac{3}{2x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}\times 3}{6\times 2x})$$

Cancel out 3x in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{4})$$

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

$$\frac{1}{4}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{4}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{4}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{4}$$