Solve 1/x/frac{x{11}}=

$$\frac { \frac { 1 } { x } } { \frac { x } { 11 } } =$$

Evaluate

$$\frac{11}{x^{2}}$$

Solution Steps

Divide \frac{1}{x} by \frac{x}{11} by multiplying \frac{1}{x} by the reciprocal of \frac{x}{11}.

$$\frac{11}{xx}$$

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

$$\frac{11}{x^{2}}$$

Differentiate w.r.t. x

$$-\frac{22}{x^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{1}{11}}x^{-1-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{-2})$$

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}.

$$-2\times 11x^{-2-1}$$

Do the arithmetic.

$$-22x^{-3}$$