Solve x^-1/frac{4000{40000}}

$$\frac{ { x }^{ -1 } }{ \frac{ 4000 }{ 40000 } }$$

Evaluate

$$\frac{10}{x}$$

Solution Steps

Divide x^{-1} by \frac{4000}{40000} by multiplying x^{-1} by the reciprocal of \frac{4000}{40000}.

$$\frac{x^{-1}\times 40000}{4000}$$

Divide x^{-1}\times 40000 by 4000 to get x^{-1}\times 10.

$$x^{-1}\times 10$$

Differentiate w.r.t. x

$$-\frac{10}{x^{2}}$$

Steps Using Definition of a Derivative

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

$$-10x^{-1-1}$$

Subtract 1 from -1.

$$-10x^{-2}$$