Solve a*a*a*a

$$a \cdot a \cdot a \cdot a$$

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.

$$4a^{3}$$