Solve nsqrt{sqrt{256}}=

$$n \sqrt { \sqrt { 256 } } =$$

Evaluate

$$4n$$

Solution Steps

Calculate the square root of 256 and get 16.

$$n\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$n\times 4$$

Differentiate w.r.t. n

$$4$$

Steps Using Definition of a Derivative

Calculate the square root of 256 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\sqrt{16})$$

Calculate the square root of 16 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times 4)$$

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

$$4n^{1-1}$$

Subtract 1 from 1.

$$4n^{0}$$

For any term t except 0, t^{0}=1.

$$4\times 1$$

For any term t, t\times 1=t and 1t=t.

$$4$$