Solve 3/2(frac{3{2x})}

$$\frac { 3 } { 2 ( \frac { 3 } { 2 x } ) }$$

Evaluate

$$x$$

Solution Steps

Express 2\times \frac{3}{2x} as a single fraction.

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

Cancel out 2 in both numerator and denominator.

$$\frac{3}{\frac{3}{x}}$$

Divide 3 by \frac{3}{x} by multiplying 3 by the reciprocal of \frac{3}{x}.

$$\frac{3x}{3}$$

Cancel out 3 and 3.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Express 2\times \frac{3}{2x} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{\frac{2\times 3}{2x}})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{\frac{3}{x}})$$

Divide 3 by \frac{3}{x} by multiplying 3 by the reciprocal of \frac{3}{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x}{3})$$

Cancel out 3 and 3.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$