Solve 1/x1/dx

$$\frac { 1 } { x } \frac { 1 } { d x }$$

Evaluate

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

Solution Steps

Multiply \frac{1}{x} times \frac{1}{dx} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{xdx}$$

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

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

Differentiate w.r.t. x

$$-\frac{2}{dx^{3}}$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\left(-\frac{2}{d}\right)x^{-3}$$