Solve n^-1(14/2*35.31)

$$n ^ { - 1 } ( \frac { 14 } { 2 \times 35.31 } )$$

Evaluate

$$\frac{700}{3531n}$$

Solution Steps

Multiply 2 and 35.31 to get 70.62.

$$n^{-1}\times \frac{14}{70.62}$$

Expand \frac{14}{70.62} by multiplying both numerator and the denominator by 100.

$$n^{-1}\times \frac{1400}{7062}$$

Reduce the fraction \frac{1400}{7062} to lowest terms by extracting and canceling out 2.

$$n^{-1}\times \frac{700}{3531}$$

Differentiate w.r.t. n

$$-\frac{700}{3531n^{2}}$$

Steps Using Definition of a Derivative

Multiply 2 and 35.31 to get 70.62.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{-1}\times \frac{14}{70.62})$$

Expand \frac{14}{70.62} by multiplying both numerator and the denominator by 100.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{-1}\times \frac{1400}{7062})$$

Reduce the fraction \frac{1400}{7062} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{-1}\times \frac{700}{3531})$$

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

$$-\frac{700}{3531}n^{-1-1}$$

Subtract 1 from -1.

$$-\frac{700}{3531}n^{-2}$$