Solve n^-3/n^3

$$\frac { n ^ { - 3 } } { n ^ { 3 } }$$

Differentiate w.r.t. n

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{1}n^{-3-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{-6})$$

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}.

$$-6n^{-6-1}$$

Do the arithmetic.

$$-6n^{-7}$$

Evaluate

$$\frac{1}{n^{6}}$$

Solution Steps

Rewrite n^{3} as n^{-3}n^{6}. Cancel out n^{-3} in both numerator and denominator.

$$\frac{1}{n^{6}}$$