Solve x/x^3

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

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

$$x^{1-3}$$

Subtract 3 from 1.

$$x^{-2}$$

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{1-3})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-2x^{-3}$$