Solve 1/x/2x

$$\frac{ \frac{ 1 }{ x } }{ 2x }$$

Evaluate

$$\frac{1}{2x^{2}}$$

Solution Steps

Express \frac{\frac{1}{x}}{2x} as a single fraction.

$$\frac{1}{x\times 2x}$$

Multiply x and x to get x^{2}.

$$\frac{1}{x^{2}\times 2}$$

Differentiate w.r.t. x

$$-\frac{1}{x^{3}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{-1-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{-2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-2\times \frac{1}{2}x^{-2-1}$$

Do the arithmetic.

$$-x^{-3}$$