Solve 7200/xdiv400/8

$$\frac { 7200 } { x } \div \frac { 400 } { 8 }$$

Evaluate

$$\frac{144}{x}$$

Solution Steps

Divide \frac{7200}{x} by \frac{400}{8} by multiplying \frac{7200}{x} by the reciprocal of \frac{400}{8}.

$$\frac{7200\times 8}{x\times 400}$$

Cancel out 400 in both numerator and denominator.

$$\frac{8\times 18}{x}$$

Multiply 8 and 18 to get 144.

$$\frac{144}{x}$$

Differentiate w.r.t. x

$$-\frac{144}{x^{2}}$$

Steps Using Definition of a Derivative

Divide \frac{7200}{x} by \frac{400}{8} by multiplying \frac{7200}{x} by the reciprocal of \frac{400}{8}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7200\times 8}{x\times 400})$$

Cancel out 400 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8\times 18}{x})$$

Multiply 8 and 18 to get 144.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{144}{x})$$

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

$$-144x^{-1-1}$$

Subtract 1 from -1.

$$-144x^{-2}$$