Solve x^-12/x^-7

$$\frac { x ^ { - 12 } } { x ^ { - 7 } }$$

Differentiate w.r.t. x

$$-\frac{5}{x^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{-12-\left(-7\right)})$$

Do the arithmetic.

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

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}.

$$-5x^{-5-1}$$

Do the arithmetic.

$$-5x^{-6}$$

Evaluate

$$\frac{1}{x^{5}}$$

Solution Steps

Rewrite x^{-7} as x^{-12}x^{5}. Cancel out x^{-12} in both numerator and denominator.

$$\frac{1}{x^{5}}$$