Solve n11405/441573

$$n \frac{ 11405 }{ 441 } 573$$

Evaluate

$$\frac{2178355n}{147}$$

Solution Steps

Express \frac{11405}{441}\times 573 as a single fraction.

$$n\times \frac{11405\times 573}{441}$$

Multiply 11405 and 573 to get 6535065.

$$n\times \frac{6535065}{441}$$

Reduce the fraction \frac{6535065}{441} to lowest terms by extracting and canceling out 3.

$$n\times \frac{2178355}{147}$$

Differentiate w.r.t. n

$$\frac{2178355}{147} = 14818\frac{109}{147} = 14818.741496598639$$

Steps Using Definition of a Derivative

Express \frac{11405}{441}\times 573 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{11405\times 573}{441})$$

Multiply 11405 and 573 to get 6535065.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{6535065}{441})$$

Reduce the fraction \frac{6535065}{441} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n\times \frac{2178355}{147})$$

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

$$\frac{2178355}{147}n^{1-1}$$

Subtract 1 from 1.

$$\frac{2178355}{147}n^{0}$$

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

$$\frac{2178355}{147}\times 1$$

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

$$\frac{2178355}{147}$$