Solve a*6*a*a

$$a \times 6 \times a \times a$$

Evaluate

$$6a^{3}$$

Solution Steps

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

$$a^{2}\times 6a$$

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

$$a^{3}\times 6$$

Differentiate w.r.t. a

$$18a^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{2}\times 6a)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{3}\times 6)$$

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

$$3\times 6a^{3-1}$$

Multiply 3 times 6.

$$18a^{3-1}$$

Subtract 1 from 3.

$$18a^{2}$$