Solve y/y^-2

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

Differentiate w.r.t. y

$$3y^{2}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{3})$$

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}.

$$3y^{3-1}$$

Do the arithmetic.

$$3y^{2}$$

Evaluate

$$y^{3}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 1 to get 3.

$$y^{3}$$