Solve 3.14Y(3.14/2*314)*4

$$3.14 Y ( \frac { 3.14 } { 2 \times 314 } ) \times 4$$

Evaluate

$$\frac{157Y}{2500}$$

Solution Steps

Multiply 2 and 314 to get 628.

$$3.14Y\times \frac{3.14}{628}\times 4$$

Expand \frac{3.14}{628} by multiplying both numerator and the denominator by 100.

$$3.14Y\times \frac{314}{62800}\times 4$$

Reduce the fraction \frac{314}{62800} to lowest terms by extracting and canceling out 314.

$$3.14Y\times \frac{1}{200}\times 4$$

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$\frac{157}{50}Y\times \frac{1}{200}\times 4$$

Multiply \frac{157}{50} times \frac{1}{200} by multiplying numerator times numerator and denominator times denominator.

$$\frac{157\times 1}{50\times 200}Y\times 4$$

Do the multiplications in the fraction \frac{157\times 1}{50\times 200}.

$$\frac{157}{10000}Y\times 4$$

Express \frac{157}{10000}\times 4 as a single fraction.

$$\frac{157\times 4}{10000}Y$$

Multiply 157 and 4 to get 628.

$$\frac{628}{10000}Y$$

Reduce the fraction \frac{628}{10000} to lowest terms by extracting and canceling out 4.

$$\frac{157}{2500}Y$$

Differentiate w.r.t. Y

$$0.0628$$

Steps Using Definition of a Derivative

Multiply 2 and 314 to get 628.

$$\frac{\mathrm{d}}{\mathrm{d}Y}(3.14Y\times \frac{3.14}{628}\times 4)$$

Expand \frac{3.14}{628} by multiplying both numerator and the denominator by 100.

$$\frac{\mathrm{d}}{\mathrm{d}Y}(3.14Y\times \frac{314}{62800}\times 4)$$

Reduce the fraction \frac{314}{62800} to lowest terms by extracting and canceling out 314.

$$\frac{\mathrm{d}}{\mathrm{d}Y}(3.14Y\times \frac{1}{200}\times 4)$$

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}Y}(\frac{157}{50}Y\times \frac{1}{200}\times 4)$$

Multiply \frac{157}{50} times \frac{1}{200} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}Y}(\frac{157\times 1}{50\times 200}Y\times 4)$$

Do the multiplications in the fraction \frac{157\times 1}{50\times 200}.

$$\frac{\mathrm{d}}{\mathrm{d}Y}(\frac{157}{10000}Y\times 4)$$

Express \frac{157}{10000}\times 4 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}Y}(\frac{157\times 4}{10000}Y)$$

Multiply 157 and 4 to get 628.

$$\frac{\mathrm{d}}{\mathrm{d}Y}(\frac{628}{10000}Y)$$

Reduce the fraction \frac{628}{10000} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}Y}(\frac{157}{2500}Y)$$

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

$$\frac{157}{2500}Y^{1-1}$$

Subtract 1 from 1.

$$\frac{157}{2500}Y^{0}$$

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

$$\frac{157}{2500}\times 1$$

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

$$\frac{157}{2500}$$