Solve 2*3.14*(55/2/10)*(1600/1b)

$$2 * 3.14 * ( 55 / 2 / 10 ) * ( 1600 / 1 b )$$

Evaluate

$$27632b$$

Solution Steps

Multiply 2 and 3.14 to get 6.28.

$$6.28\times \frac{\frac{55}{2}}{10}\times \frac{1600}{1}b$$

Express \frac{\frac{55}{2}}{10} as a single fraction.

$$6.28\times \frac{55}{2\times 10}\times \frac{1600}{1}b$$

Multiply 2 and 10 to get 20.

$$6.28\times \frac{55}{20}\times \frac{1600}{1}b$$

Reduce the fraction \frac{55}{20} to lowest terms by extracting and canceling out 5.

$$6.28\times \frac{11}{4}\times \frac{1600}{1}b$$

Convert decimal number 6.28 to fraction \frac{628}{100}. Reduce the fraction \frac{628}{100} to lowest terms by extracting and canceling out 4.

$$\frac{157}{25}\times \frac{11}{4}\times \frac{1600}{1}b$$

Multiply \frac{157}{25} times \frac{11}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{157\times 11}{25\times 4}\times \frac{1600}{1}b$$

Do the multiplications in the fraction \frac{157\times 11}{25\times 4}.

$$\frac{1727}{100}\times \frac{1600}{1}b$$

Anything divided by one gives itself.

$$\frac{1727}{100}\times 1600b$$

Express \frac{1727}{100}\times 1600 as a single fraction.

$$\frac{1727\times 1600}{100}b$$

Multiply 1727 and 1600 to get 2763200.

$$\frac{2763200}{100}b$$

Divide 2763200 by 100 to get 27632.

$$27632b$$

Differentiate w.r.t. b

$$27632$$

Steps Using Definition of a Derivative

Multiply 2 and 3.14 to get 6.28.

$$\frac{\mathrm{d}}{\mathrm{d}b}(6.28\times \frac{\frac{55}{2}}{10}\times \frac{1600}{1}b)$$

Express \frac{\frac{55}{2}}{10} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}b}(6.28\times \frac{55}{2\times 10}\times \frac{1600}{1}b)$$

Multiply 2 and 10 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}b}(6.28\times \frac{55}{20}\times \frac{1600}{1}b)$$

Reduce the fraction \frac{55}{20} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}b}(6.28\times \frac{11}{4}\times \frac{1600}{1}b)$$

Convert decimal number 6.28 to fraction \frac{628}{100}. Reduce the fraction \frac{628}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{157}{25}\times \frac{11}{4}\times \frac{1600}{1}b)$$

Multiply \frac{157}{25} times \frac{11}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{157\times 11}{25\times 4}\times \frac{1600}{1}b)$$

Do the multiplications in the fraction \frac{157\times 11}{25\times 4}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1727}{100}\times \frac{1600}{1}b)$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1727}{100}\times 1600b)$$

Express \frac{1727}{100}\times 1600 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1727\times 1600}{100}b)$$

Multiply 1727 and 1600 to get 2763200.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{2763200}{100}b)$$

Divide 2763200 by 100 to get 27632.

$$\frac{\mathrm{d}}{\mathrm{d}b}(27632b)$$

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

$$27632b^{1-1}$$

Subtract 1 from 1.

$$27632b^{0}$$

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

$$27632\times 1$$

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

$$27632$$