Solve 1/4(t1/2)

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

Evaluate

$$\frac{t}{8}$$

Solution Steps

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

$$\frac{1\times 1}{4\times 2}t$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 2}.

$$\frac{1}{8}t$$

Differentiate w.r.t. t

$$\frac{1}{8} = 0.125$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{1\times 1}{4\times 2}t)$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 2}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{1}{8}t)$$

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

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

Subtract 1 from 1.

$$\frac{1}{8}t^{0}$$

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

$$\frac{1}{8}\times 1$$

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

$$\frac{1}{8}$$