Solve 4a^4*2a^2

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

Evaluate

$$8a^{6}$$

Solution Steps

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

$$4a^{6}\times 2$$

Multiply 4 and 2 to get 8.

$$8a^{6}$$

Differentiate w.r.t. a

$$48a^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{6}\times 2)$$

Multiply 4 and 2 to get 8.

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

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

$$6\times 8a^{6-1}$$

Multiply 6 times 8.

$$48a^{6-1}$$

Subtract 1 from 6.

$$48a^{5}$$