Solve AAAA

$$A A A A$$

Evaluate

$$A^{4}$$

Solution Steps

Multiply A and A to get A^{2}.

$$A^{2}AA$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$A^{3}A$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$A^{4}$$

Differentiate w.r.t. A

$$4A^{3}$$

Steps Using Definition of a Derivative

Multiply A and A to get A^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A^{2}AA)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A^{3}A)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A^{4})$$

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

$$4A^{4-1}$$

Subtract 1 from 4.

$$4A^{3}$$