Solve a^-1/a^2

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

Differentiate w.r.t. a

$$-\frac{3}{a^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{-1-2})$$

Do the arithmetic.

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

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}.

$$-3a^{-3-1}$$

Do the arithmetic.

$$-3a^{-4}$$

Evaluate

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

Solution Steps

Rewrite a^{2} as a^{-1}a^{3}. Cancel out a^{-1} in both numerator and denominator.

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