Solve a^2*a^4*(2a^6)

$$a ^ { 2 } \cdot a ^ { 4 } \cdot ( 2 a ^ { 6 } )$$

Evaluate

$$2a^{12}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$a^{12}\times 2$$

Differentiate w.r.t. a

$$24a^{11}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{12}\times 2)$$

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

$$12\times 2a^{12-1}$$

Multiply 12 times 2.

$$24a^{12-1}$$

Subtract 1 from 12.

$$24a^{11}$$