Solve 24/xdiv12/x^2=

$$\frac { 24 } { x } \div \frac { 12 } { x ^ { 2 } } =$$

Evaluate

$$2x$$

Solution Steps

Divide \frac{24}{x} by \frac{12}{x^{2}} by multiplying \frac{24}{x} by the reciprocal of \frac{12}{x^{2}}.

$$\frac{24x^{2}}{x\times 12}$$

Cancel out 12x in both numerator and denominator.

$$2x$$

Differentiate w.r.t. x

$$2$$

Steps Using Definition of a Derivative

Divide \frac{24}{x} by \frac{12}{x^{2}} by multiplying \frac{24}{x} by the reciprocal of \frac{12}{x^{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24x^{2}}{x\times 12})$$

Cancel out 12x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x)$$

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

$$2x^{1-1}$$

Subtract 1 from 1.

$$2x^{0}$$

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

$$2\times 1$$

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

$$2$$