Solve c*(-5/6)div(-1/4

$$c \cdot ( - \frac { 5 } { 6 } ) \div ( - \frac { 1 } { 4 }$$

Evaluate

$$\frac{10c}{3}$$

Solution Steps

Divide c\left(-\frac{5}{6}\right) by -\frac{1}{4} by multiplying c\left(-\frac{5}{6}\right) by the reciprocal of -\frac{1}{4}.

$$\frac{c\left(-\frac{5}{6}\right)\times 4}{-1}$$

Express -\frac{5}{6}\times 4 as a single fraction.

$$\frac{c\times \frac{-5\times 4}{6}}{-1}$$

Multiply -5 and 4 to get -20.

$$\frac{c\times \frac{-20}{6}}{-1}$$

Reduce the fraction \frac{-20}{6} to lowest terms by extracting and canceling out 2.

$$\frac{c\left(-\frac{10}{3}\right)}{-1}$$

Anything divided by -1 gives its opposite.

$$-c\left(-\frac{10}{3}\right)$$

Multiply -1 and -\frac{10}{3} to get \frac{10}{3}.

$$\frac{10}{3}c$$

Differentiate w.r.t. c

$$\frac{10}{3} = 3\frac{1}{3} = 3.3333333333333335$$

Steps Using Definition of a Derivative

Divide c\left(-\frac{5}{6}\right) by -\frac{1}{4} by multiplying c\left(-\frac{5}{6}\right) by the reciprocal of -\frac{1}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{c\left(-\frac{5}{6}\right)\times 4}{-1})$$

Express -\frac{5}{6}\times 4 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{c\times \frac{-5\times 4}{6}}{-1})$$

Multiply -5 and 4 to get -20.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{c\times \frac{-20}{6}}{-1})$$

Reduce the fraction \frac{-20}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{c\left(-\frac{10}{3}\right)}{-1})$$

Anything divided by -1 gives its opposite.

$$\frac{\mathrm{d}}{\mathrm{d}c}(-c\left(-\frac{10}{3}\right))$$

Multiply -1 and -\frac{10}{3} to get \frac{10}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{10}{3}c)$$

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

$$\frac{10}{3}c^{1-1}$$

Subtract 1 from 1.

$$\frac{10}{3}c^{0}$$

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

$$\frac{10}{3}\times 1$$

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

$$\frac{10}{3}$$