Solve a^3*2a^3*3a^3

$$a ^ { 3 } \times 2 a ^ { 3 } \times 3 a ^ { 3 }$$

Evaluate

$$6a^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$a^{6}\times 2\times 3a^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$a^{9}\times 2\times 3$$

Multiply 2 and 3 to get 6.

$$a^{9}\times 6$$

Differentiate w.r.t. a

$$54a^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}\times 2\times 3a^{3})$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{9}\times 2\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{9}\times 6)$$

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

$$9\times 6a^{9-1}$$

Multiply 9 times 6.

$$54a^{9-1}$$

Subtract 1 from 9.

$$54a^{8}$$