Solve y^-6/y^7

$$\frac { y ^ { - 6 } } { y ^ { 7 } }$$

Differentiate w.r.t. y

$$-\frac{13}{y^{14}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{-6-7})$$

Do the arithmetic.

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

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}.

$$-13y^{-13-1}$$

Do the arithmetic.

$$-13y^{-14}$$

Evaluate

$$\frac{1}{y^{13}}$$

Solution Steps

Rewrite y^{7} as y^{-6}y^{13}. Cancel out y^{-6} in both numerator and denominator.

$$\frac{1}{y^{13}}$$