Solve n(360/365.2422*78)

$$n ( \frac { 360 } { 365.2422 } \times 78 )$$

Evaluate

$$\frac{46800000n}{608737}$$

Solution Steps

Expand \frac{360}{365.2422} by multiplying both numerator and the denominator by 10000.

$$n\times \frac{3600000}{3652422}\times 78$$

Reduce the fraction \frac{3600000}{3652422} to lowest terms by extracting and canceling out 6.

$$n\times \frac{600000}{608737}\times 78$$

Express \frac{600000}{608737}\times 78 as a single fraction.

$$n\times \frac{600000\times 78}{608737}$$

Multiply 600000 and 78 to get 46800000.

$$n\times \frac{46800000}{608737}$$

Differentiate w.r.t. n

$$\frac{46800000}{608737} = 76\frac{535988}{608737} = 76.88049190372854$$

Steps Using Definition of a Derivative

Expand \frac{360}{365.2422} by multiplying both numerator and the denominator by 10000.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{3600000}{3652422}\times 78)$$

Reduce the fraction \frac{3600000}{3652422} to lowest terms by extracting and canceling out 6.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{600000}{608737}\times 78)$$

Express \frac{600000}{608737}\times 78 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{600000\times 78}{608737})$$

Multiply 600000 and 78 to get 46800000.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{46800000}{608737})$$

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

$$\frac{46800000}{608737}n^{1-1}$$

Subtract 1 from 1.

$$\frac{46800000}{608737}n^{0}$$

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

$$\frac{46800000}{608737}\times 1$$

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

$$\frac{46800000}{608737}$$