Solve x^-9/x^9

$$\frac { x ^ { - 9 } } { x ^ { 9 } }$$

Differentiate w.r.t. x

$$-\frac{18}{x^{19}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{-9-9})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-18})$$

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}.

$$-18x^{-18-1}$$

Do the arithmetic.

$$-18x^{-19}$$

Evaluate

$$\frac{1}{x^{18}}$$

Solution Steps

Rewrite x^{9} as x^{-9}x^{18}. Cancel out x^{-9} in both numerator and denominator.

$$\frac{1}{x^{18}}$$