Solve 1/3(frac{1{3x})}

$$\frac{ 1 }{ 3( \frac{ 1 }{ 3x } ) }$$

Evaluate

$$x$$

Solution Steps

Express 3\times \frac{1}{3x} as a single fraction.

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

Divide 1 by \frac{3}{3x} by multiplying 1 by the reciprocal of \frac{3}{3x}.

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

Cancel out 3 and 3.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Express 3\times \frac{1}{3x} as a single fraction.

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

Divide 1 by \frac{3}{3x} by multiplying 1 by the reciprocal of \frac{3}{3x}.

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

Cancel out 3 and 3.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$