Solve (a^-2/2b^0)_-2^-3*sqrt[3]{a^6}

$$( \frac { a ^ { - 2 } } { 2 b ^ { 0 } } ) _ { - 2 } ^ { - 3 } \times \sqrt[ 3 ] { a ^ { 6 } }$$

Evaluate

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

Solution Steps

Calculate b to the power of 0 and get 1.

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

Multiply 2 and 1 to get 2.

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

Differentiate w.r.t. a

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

Steps Using Definition of a Derivative

Calculate b to the power of 0 and get 1.

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

Multiply 2 and 1 to get 2.

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

The derivative of ax^{n} is nax^{n-1}.

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

Multiply -2 times \frac{1}{2}.

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

Subtract 1 from -2.

$$-a^{-3}$$