Solve (2)a^10*a^2*a

$$( 2 ) a ^ { 10 } \cdot a ^ { 2 } \cdot a$$

Evaluate

$$2a^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 10 and 2 to get 12.

$$2a^{12}a$$

To multiply powers of the same base, add their exponents. Add 12 and 1 to get 13.

$$2a^{13}$$

Differentiate w.r.t. a

$$26a^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 10 and 2 to get 12.

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

To multiply powers of the same base, add their exponents. Add 12 and 1 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{13})$$

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

$$13\times 2a^{13-1}$$

Multiply 13 times 2.

$$26a^{13-1}$$

Subtract 1 from 13.

$$26a^{12}$$