Solve 1/2*x/3

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

Evaluate

$$\frac{x}{6}$$

Solution Steps

Multiply \frac{1}{2} times \frac{x}{3} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{x}{6}$$

Differentiate w.r.t. x

$$\frac{1}{6} = 0.16666666666666666$$

Steps Using Definition of a Derivative

Multiply \frac{1}{2} times \frac{x}{3} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{6})$$

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

$$\frac{1}{6}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{6}x^{0}$$

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

$$\frac{1}{6}\times 1$$

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

$$\frac{1}{6}$$