Solve 1/6(-frac{1{6x})}

$$\frac{ 1 }{ 6(- \frac{ 1 }{ 6x } ) }$$

Differentiate w.r.t. x

$$-1$$

Steps Using Definition of a Derivative

Express 6\left(-\frac{1}{6x}\right) as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{-6}{6x}})$$

Cancel out 6 in both numerator and denominator.

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

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

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

Anything divided by -1 gives its opposite.

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

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.

$$-1$$

Evaluate

$$-x$$