Solve 40/frac{x{60}}=

$$\frac { 40 } { \frac { x } { 60 } } =$$

Evaluate

$$\frac{2400}{x}$$

Solution Steps

Divide 40 by \frac{x}{60} by multiplying 40 by the reciprocal of \frac{x}{60}.

$$\frac{40\times 60}{x}$$

Multiply 40 and 60 to get 2400.

$$\frac{2400}{x}$$

Differentiate w.r.t. x

$$-\frac{2400}{x^{2}}$$

Steps Using Definition of a Derivative

Divide 40 by \frac{x}{60} by multiplying 40 by the reciprocal of \frac{x}{60}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{40\times 60}{x})$$

Multiply 40 and 60 to get 2400.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2400}{x})$$

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

$$-2400x^{-1-1}$$

Subtract 1 from -1.

$$-2400x^{-2}$$