Solve a*a^10+a^3*a^8

$$a \cdot a ^ { 10 } + a ^ { 3 } \cdot a ^ { 8 }$$

Evaluate

$$2a^{11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 10 to get 11.

$$a^{11}+a^{3}a^{8}$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$a^{11}+a^{11}$$

Combine a^{11} and a^{11} to get 2a^{11}.

$$2a^{11}$$

Differentiate w.r.t. a

$$22a^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 10 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{11}+a^{3}a^{8})$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{11}+a^{11})$$

Combine a^{11} and a^{11} to get 2a^{11}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{11})$$

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

$$11\times 2a^{11-1}$$

Multiply 11 times 2.

$$22a^{11-1}$$

Subtract 1 from 11.

$$22a^{10}$$