Solve y/y^2=

$$\frac { y } { y ^ { 2 } } =$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

$$y^{1-2}$$

Subtract 2 from 1.

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

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.

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

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.

$$-y^{-2}$$