Solve frac{{left({A}_{12}right)}^6}{12^6}=

$$\frac{ { \left( { A }_{ 12 } \right) }^{ 6 } }{ { 12 }^{ 6 } } =$$

Differentiate w.r.t. A_12

$$\frac{A_{12}^{5}}{497664}$$

Steps Using Definition of a Derivative

Calculate 12 to the power of 6 and get 2985984.

$$\frac{\mathrm{d}}{\mathrm{d}A_{12}}(\frac{A_{12}^{6}}{2985984})$$

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

$$6\times \frac{1}{2985984}A_{12}^{6-1}$$

Multiply 6 times \frac{1}{2985984}.

$$\frac{1}{497664}A_{12}^{6-1}$$

Subtract 1 from 6.

$$\frac{1}{497664}A_{12}^{5}$$

Evaluate

$$\frac{A_{12}^{6}}{2985984}$$

Solution Steps

Calculate 12 to the power of 6 and get 2985984.

$$\frac{A_{12}^{6}}{2985984}$$