Solve 2c/5*10/36

$$\frac { 2 c } { 5 } \times \frac { 10 } { 36 }$$

Evaluate

$$\frac{c}{9}$$

Solution Steps

Reduce the fraction \frac{10}{36} to lowest terms by extracting and canceling out 2.

$$\frac{2c}{5}\times \frac{5}{18}$$

Multiply \frac{2c}{5} times \frac{5}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2c\times 5}{5\times 18}$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{c}{9}$$

Differentiate w.r.t. c

$$\frac{1}{9} = 0.1111111111111111$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{10}{36} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{2c}{5}\times \frac{5}{18})$$

Multiply \frac{2c}{5} times \frac{5}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{2c\times 5}{5\times 18})$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{c}{9})$$

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

$$\frac{1}{9}c^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{9}c^{0}$$

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

$$\frac{1}{9}\times 1$$

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

$$\frac{1}{9}$$