Solve [y^-1x^-2/y^-2x^-2]

$$[ \frac { y ^ { - 1 } x ^ { - 2 } } { y ^ { - 2 } x ^ { - 2 } } ]$$

Evaluate

$$y$$

Solution Steps

Cancel out x^{-2} in both numerator and denominator.

$$\frac{\frac{1}{y}}{y^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$y^{1}$$

Calculate y to the power of 1 and get y.

$$y$$

Differentiate w.r.t. y

$$1$$

Steps Using Definition of a Derivative

Cancel out x^{-2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\frac{1}{y}}{y^{-2}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{1})$$

Calculate y to the power of 1 and get y.

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

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

$$y^{1-1}$$

Subtract 1 from 1.

$$y^{0}$$

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

$$1$$