Solve 1/2(t^2/4)

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

Evaluate

$$\frac{t^{2}}{8}$$

Solution Steps

Multiply \frac{1}{2} times \frac{t^{2}}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{t^{2}}{2\times 4}$$

Multiply 2 and 4 to get 8.

$$\frac{t^{2}}{8}$$

Differentiate w.r.t. t

$$\frac{t}{4}$$

Steps Using Definition of a Derivative

Multiply \frac{1}{2} times \frac{t^{2}}{4} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{t^{2}}{8})$$

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

$$2\times \frac{1}{8}t^{2-1}$$

Multiply 2 times \frac{1}{8}.

$$\frac{1}{4}t^{2-1}$$

Subtract 1 from 2.

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

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

$$\frac{1}{4}t$$