Solve A*4^16div12

$$A \times 4 ^ { 16 } \div 12$$

Evaluate

$$\frac{1073741824A}{3}$$

Solution Steps

Calculate 4 to the power of 16 and get 4294967296.

$$\frac{A\times 4294967296}{12}$$

Divide A\times 4294967296 by 12 to get A\times \frac{1073741824}{3}.

$$A\times \frac{1073741824}{3}$$

Differentiate w.r.t. A

$$\frac{1073741824}{3} = 357913941\frac{1}{3} = 357913941.3333333$$

Steps Using Definition of a Derivative

Calculate 4 to the power of 16 and get 4294967296.

$$\frac{\mathrm{d}}{\mathrm{d}A}(\frac{A\times 4294967296}{12})$$

Divide A\times 4294967296 by 12 to get A\times \frac{1073741824}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times \frac{1073741824}{3})$$

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

$$\frac{1073741824}{3}A^{1-1}$$

Subtract 1 from 1.

$$\frac{1073741824}{3}A^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1073741824}{3}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1073741824}{3}$$