Solve n(360/3652422*78)

$$n ( \frac { 360 } { 3652422 } \times 78 )$$

Evaluate

$$\frac{4680n}{608737}$$

Solution Steps

Reduce the fraction \frac{360}{3652422} to lowest terms by extracting and canceling out 6.

$$n\times \frac{60}{608737}\times 78$$

Express \frac{60}{608737}\times 78 as a single fraction.

$$n\times \frac{60\times 78}{608737}$$

Multiply 60 and 78 to get 4680.

$$n\times \frac{4680}{608737}$$

Differentiate w.r.t. n

$$\frac{4680}{608737} = 0.007688049190372854$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{360}{3652422} to lowest terms by extracting and canceling out 6.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{60}{608737}\times 78)$$

Express \frac{60}{608737}\times 78 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{60\times 78}{608737})$$

Multiply 60 and 78 to get 4680.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{4680}{608737})$$

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

$$\frac{4680}{608737}n^{1-1}$$

Subtract 1 from 1.

$$\frac{4680}{608737}n^{0}$$

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

$$\frac{4680}{608737}\times 1$$

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

$$\frac{4680}{608737}$$