Solve x^4/x^5

$$\frac { x ^ { 4 } } { x ^ { 5 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{4}}{x^{5}}$$

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

$$x^{4-5}$$

Subtract 5 from 4.

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{4-5})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-x^{-2}$$