Solve a^2a^4+(a^3)^2

$$a ^ { 2 } a ^ { 4 } + ( a ^ { 3 } ) ^ { 2 }$$

Evaluate

$$2a^{6}$$

Solution Steps

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

$$a^{6}+\left(a^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$a^{6}+a^{6}$$

Combine a^{6} and a^{6} to get 2a^{6}.

$$2a^{6}$$

Differentiate w.r.t. a

$$12a^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}+\left(a^{3}\right)^{2})$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

Combine a^{6} and a^{6} to get 2a^{6}.

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

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

$$6\times 2a^{6-1}$$

Multiply 6 times 2.

$$12a^{6-1}$$

Subtract 1 from 6.

$$12a^{5}$$