Solve 1/4(n^2)^2

$$\frac { 1 } { 4 } ( n ^ { 2 } ) ^ { 2 }$$

Differentiate w.r.t. n

$$n^{3}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{4}n^{4})$$

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

$$4\times \frac{1}{4}n^{4-1}$$

Multiply 4 times \frac{1}{4}.

$$n^{4-1}$$

Subtract 1 from 4.

$$n^{3}$$

Evaluate

$$\frac{n^{4}}{4}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{1}{4}n^{4}$$