Solve 3^2k^-6k^4

$$3 ^ { 2 } k ^ { - 6 } k ^ { 4 }$$

Evaluate

$$\frac{9}{k^{2}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -6 and 4 to get -2.

$$3^{2}k^{-2}$$

Calculate 3 to the power of 2 and get 9.

$$9k^{-2}$$

Differentiate w.r.t. k

$$-\frac{18}{k^{3}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -6 and 4 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}k}(3^{2}k^{-2})$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}k}(9k^{-2})$$

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

$$-2\times 9k^{-2-1}$$

Multiply -2 times 9.

$$-18k^{-2-1}$$

Subtract 1 from -2.

$$-18k^{-3}$$