Solve frac{{3}4}{2/x}

$$\frac { { 3 } 4 } { \frac { 2 } { x } }$$

Evaluate

$$6x$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{12}{\frac{2}{x}}$$

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

$$\frac{12x}{2}$$

Divide 12x by 2 to get 6x.

$$6x$$

Differentiate w.r.t. x

$$6$$

Steps Using Definition of a Derivative

Multiply 3 and 4 to get 12.

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

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

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

Divide 12x by 2 to get 6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x)$$

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

$$6x^{1-1}$$

Subtract 1 from 1.

$$6x^{0}$$

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

$$6\times 1$$

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

$$6$$