Solve y^-13/y^10

$$\frac { y ^ { - 13 } } { y ^ { 10 } }$$

Differentiate w.r.t. y

$$-\frac{23}{y^{24}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{-13-10})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{-23})$$

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}.

$$-23y^{-23-1}$$

Do the arithmetic.

$$-23y^{-24}$$

Evaluate

$$\frac{1}{y^{23}}$$

Solution Steps

Rewrite y^{10} as y^{-13}y^{23}. Cancel out y^{-13} in both numerator and denominator.

$$\frac{1}{y^{23}}$$