Solve y^-5/y^-2

$$\frac { y ^ { - 5 } } { y ^ { - 2 } }$$

Differentiate w.r.t. y

$$-\frac{3}{y^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{-5-\left(-2\right)})$$

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.

$$-3y^{-4}$$

Evaluate

$$\frac{1}{y^{3}}$$

Solution Steps

Rewrite y^{-2} as y^{-5}y^{3}. Cancel out y^{-5} in both numerator and denominator.

$$\frac{1}{y^{3}}$$