Solve 2a^2*3a^4*3a^8

$$2 a ^ { 2 } \times 3 a ^ { 4 } \times 3 a ^ { 8 }$$

Evaluate

$$18a^{14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$2a^{6}\times 3\times 3a^{8}$$

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$2a^{14}\times 3\times 3$$

Multiply 2 and 3 to get 6.

$$6a^{14}\times 3$$

Multiply 6 and 3 to get 18.

$$18a^{14}$$

Differentiate w.r.t. a

$$252a^{13}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{6}\times 3\times 3a^{8})$$

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{14}\times 3\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{14}\times 3)$$

Multiply 6 and 3 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}a}(18a^{14})$$

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

$$14\times 18a^{14-1}$$

Multiply 14 times 18.

$$252a^{14-1}$$

Subtract 1 from 14.

$$252a^{13}$$