Solve 108/360*2*3.1y

$$\frac { 108 } { 360 } \times 2 \times 3.1 y$$

Evaluate

$$\frac{93y}{50}$$

Solution Steps

Reduce the fraction \frac{108}{360} to lowest terms by extracting and canceling out 36.

$$\frac{3}{10}\times 2\times 3.1y$$

Express \frac{3}{10}\times 2 as a single fraction.

$$\frac{3\times 2}{10}\times 3.1y$$

Multiply 3 and 2 to get 6.

$$\frac{6}{10}\times 3.1y$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{3}{5}\times 3.1y$$

Convert decimal number 3.1 to fraction \frac{31}{10}.

$$\frac{3}{5}\times \frac{31}{10}y$$

Multiply \frac{3}{5} times \frac{31}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 31}{5\times 10}y$$

Do the multiplications in the fraction \frac{3\times 31}{5\times 10}.

$$\frac{93}{50}y$$

Differentiate w.r.t. y

$$1.86$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{108}{360} to lowest terms by extracting and canceling out 36.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3}{10}\times 2\times 3.1y)$$

Express \frac{3}{10}\times 2 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3\times 2}{10}\times 3.1y)$$

Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{6}{10}\times 3.1y)$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3}{5}\times 3.1y)$$

Convert decimal number 3.1 to fraction \frac{31}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3}{5}\times \frac{31}{10}y)$$

Multiply \frac{3}{5} times \frac{31}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3\times 31}{5\times 10}y)$$

Do the multiplications in the fraction \frac{3\times 31}{5\times 10}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{93}{50}y)$$

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

$$\frac{93}{50}y^{1-1}$$

Subtract 1 from 1.

$$\frac{93}{50}y^{0}$$

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

$$\frac{93}{50}\times 1$$

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

$$\frac{93}{50}$$