Solve y^-2/y^-1

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

Differentiate w.r.t. y

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

Solution Steps

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

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

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-y^{-1-1}$$

Do the arithmetic.

$$-y^{-2}$$

Evaluate

$$\frac{1}{y}$$

Solution Steps

Rewrite y^{-1} as y^{-2}y. Cancel out y^{-2} in both numerator and denominator.

$$\frac{1}{y}$$