Solve c(1/8)div(1/8)*(1/8)

$$c ( \frac { 1 } { 8 } ) \div ( \frac { 1 } { 8 } ) \times ( \frac { 1 } { 8 } )$$

Evaluate

$$\frac{c}{8}$$

Solution Steps

Divide c\times \frac{1}{8} by \frac{1}{8} by multiplying c\times \frac{1}{8} by the reciprocal of \frac{1}{8}.

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

Cancel out 8 and 8.

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

Differentiate w.r.t. c

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

Steps Using Definition of a Derivative

Divide c\times \frac{1}{8} by \frac{1}{8} by multiplying c\times \frac{1}{8} by the reciprocal of \frac{1}{8}.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c\times \frac{1}{8}\times 8\times \frac{1}{8})$$

Cancel out 8 and 8.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c\times \frac{1}{8})$$

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

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

Subtract 1 from 1.

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

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.

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