Solve (a)*3/4div12/1

$$( a ) \cdot \frac { 3 } { 4 } \div \frac { 12 } { 1 }$$

Evaluate

$$\frac{a}{16}$$

Solution Steps

Divide a\times \frac{3}{4} by \frac{12}{1} by multiplying a\times \frac{3}{4} by the reciprocal of \frac{12}{1}.

$$\frac{a\times \frac{3}{4}}{12}$$

Divide a\times \frac{3}{4} by 12 to get a\times \frac{1}{16}.

$$a\times \frac{1}{16}$$

Differentiate w.r.t. a

$$\frac{1}{16} = 0.0625$$

Steps Using Definition of a Derivative

Divide a\times \frac{3}{4} by \frac{12}{1} by multiplying a\times \frac{3}{4} by the reciprocal of \frac{12}{1}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a\times \frac{3}{4}}{12})$$

Divide a\times \frac{3}{4} by 12 to get a\times \frac{1}{16}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a\times \frac{1}{16})$$

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

$$\frac{1}{16}a^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{16}a^{0}$$

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

$$\frac{1}{16}\times 1$$

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

$$\frac{1}{16}$$