Solve 1/4text{a}5/8

$$\frac { 1 } { 4 } \text { a } \frac { 5 } { 8 }$$

Evaluate

$$\frac{5a}{32}$$

Solution Steps

Multiply \frac{1}{4} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{4\times 8}a$$

Do the multiplications in the fraction \frac{1\times 5}{4\times 8}.

$$\frac{5}{32}a$$

Differentiate w.r.t. a

$$\frac{5}{32} = 0.15625$$

Steps Using Definition of a Derivative

Multiply \frac{1}{4} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1\times 5}{4\times 8}a)$$

Do the multiplications in the fraction \frac{1\times 5}{4\times 8}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5}{32}a)$$

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

$$\frac{5}{32}a^{1-1}$$

Subtract 1 from 1.

$$\frac{5}{32}a^{0}$$

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

$$\frac{5}{32}\times 1$$

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

$$\frac{5}{32}$$