Solve n11.405/44.157.3

$$n \frac{ 11.405 }{ 44.1 } 57.3$$

Evaluate

$$\frac{435671n}{29400}$$

Solution Steps

Expand \frac{11.405}{44.1} by multiplying both numerator and the denominator by 1000.

$$n\times \frac{11405}{44100}\times 57.3$$

Reduce the fraction \frac{11405}{44100} to lowest terms by extracting and canceling out 5.

$$n\times \frac{2281}{8820}\times 57.3$$

Convert decimal number 57.3 to fraction \frac{573}{10}.

$$n\times \frac{2281}{8820}\times \frac{573}{10}$$

Multiply \frac{2281}{8820} times \frac{573}{10} by multiplying numerator times numerator and denominator times denominator.

$$n\times \frac{2281\times 573}{8820\times 10}$$

Do the multiplications in the fraction \frac{2281\times 573}{8820\times 10}.

$$n\times \frac{1307013}{88200}$$

Reduce the fraction \frac{1307013}{88200} to lowest terms by extracting and canceling out 3.

$$n\times \frac{435671}{29400}$$

Differentiate w.r.t. n

$$\frac{435671}{29400} = 14\frac{24071}{29400} = 14.818741496598639$$

Steps Using Definition of a Derivative

Expand \frac{11.405}{44.1} by multiplying both numerator and the denominator by 1000.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{11405}{44100}\times 57.3)$$

Reduce the fraction \frac{11405}{44100} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{2281}{8820}\times 57.3)$$

Convert decimal number 57.3 to fraction \frac{573}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{2281}{8820}\times \frac{573}{10})$$

Multiply \frac{2281}{8820} times \frac{573}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{2281\times 573}{8820\times 10})$$

Do the multiplications in the fraction \frac{2281\times 573}{8820\times 10}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{1307013}{88200})$$

Reduce the fraction \frac{1307013}{88200} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{435671}{29400})$$

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

$$\frac{435671}{29400}n^{1-1}$$

Subtract 1 from 1.

$$\frac{435671}{29400}n^{0}$$

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

$$\frac{435671}{29400}\times 1$$

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

$$\frac{435671}{29400}$$