Solve n^12n^8/n^5

$$\frac { n ^ { 12 } n ^ { 8 } } { n ^ { 5 } }$$

Evaluate

$$n^{15}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 12 and 8 to get 20.

$$\frac{n^{20}}{n^{5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 20 to get 15.

$$n^{15}$$

Differentiate w.r.t. n

$$15n^{14}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 12 and 8 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{n^{20}}{n^{5}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 20 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{15})$$

The derivative of ax^{n} is nax^{n-1}.

$$15n^{15-1}$$

Subtract 1 from 15.

$$15n^{14}$$