Solve (n^3)^2*2n^-1

$$( n ^ { 3 } ) ^ { 2 } \cdot 2 n ^ { - 1 }$$

Evaluate

$$2n^{5}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$n^{6}\times 2n^{-1}$$

To multiply powers of the same base, add their exponents. Add 6 and -1 to get 5.

$$n^{5}\times 2$$

Differentiate w.r.t. n

$$10n^{4}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{6}\times 2n^{-1})$$

To multiply powers of the same base, add their exponents. Add 6 and -1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{5}\times 2)$$

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

$$5\times 2n^{5-1}$$

Multiply 5 times 2.

$$10n^{5-1}$$

Subtract 1 from 5.

$$10n^{4}$$