Solve k^-3frac{3{3}}

$$k ^ { - 3 \frac { 3 } { 3 } }$$

Evaluate

$$\frac{1}{k^{4}}$$

Solution Steps

Multiply 3 and 3 to get 9.

$$k^{-\frac{9+3}{3}}$$

Add 9 and 3 to get 12.

$$k^{-\frac{12}{3}}$$

Divide 12 by 3 to get 4.

$$k^{-4}$$

Differentiate w.r.t. k

$$-\frac{4}{k^{5}}$$

Steps Using Definition of a Derivative

Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}k}(k^{-\frac{9+3}{3}})$$

Add 9 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}k}(k^{-\frac{12}{3}})$$

Divide 12 by 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}k}(k^{-4})$$

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

$$-4k^{-4-1}$$

Subtract 1 from -4.

$$-4k^{-5}$$