Solve (x/6)^-1=

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

Evaluate

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

Solution Steps

To raise \frac{x}{6} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 6 to the power of -1 and get \frac{1}{6}.

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

Divide x^{-1} by \frac{1}{6} by multiplying x^{-1} by the reciprocal of \frac{1}{6}.

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

Differentiate w.r.t. x

$$-\frac{6}{x^{2}}$$

Steps Using Definition of a Derivative

To raise \frac{x}{6} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 6 to the power of -1 and get \frac{1}{6}.

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

Divide x^{-1} by \frac{1}{6} by multiplying x^{-1} by the reciprocal of \frac{1}{6}.

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

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

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

Subtract 1 from -1.

$$-6x^{-2}$$