Solve d/dxleft({left(x/2right)}^4right)

$$\frac{d}{d x } \left( { \left( \frac{ x }{ 2 } \right) }^{ 4 } \right)$$

Evaluate

$$\frac{x^{3}}{4}$$

Steps Using Definition of a Derivative

To raise \frac{x}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}}{2^{4}})$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}}{16})$$

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

$$4\times \frac{1}{16}x^{4-1}$$

Multiply 4 times \frac{1}{16}.

$$\frac{1}{4}x^{4-1}$$

Subtract 1 from 4.

$$\frac{1}{4}x^{3}$$

Differentiate w.r.t. x

$$\frac{3x^{2}}{4}$$