Solve 3^(3)*3^(2)4n^-6

$$3 ^ { ( 3 ) } \cdot 3 ^ { ( 2 ) } 4 n ^ { - 6 }$$

Evaluate

$$\frac{972}{n^{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$3^{5}\times 4n^{-6}$$

Calculate 3 to the power of 5 and get 243.

$$243\times 4n^{-6}$$

Multiply 243 and 4 to get 972.

$$972n^{-6}$$

Differentiate w.r.t. n

$$-\frac{5832}{n^{7}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}n}(3^{5}\times 4n^{-6})$$

Calculate 3 to the power of 5 and get 243.

$$\frac{\mathrm{d}}{\mathrm{d}n}(243\times 4n^{-6})$$

Multiply 243 and 4 to get 972.

$$\frac{\mathrm{d}}{\mathrm{d}n}(972n^{-6})$$

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

$$-6\times 972n^{-6-1}$$

Multiply -6 times 972.

$$-5832n^{-6-1}$$

Subtract 1 from -6.

$$-5832n^{-7}$$