Solve (2a)*8a^3

$$( 2 a ) \cdot 8 a ^ { 3 }$$

Evaluate

$$16a^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$2a^{4}\times 8$$

Multiply 2 and 8 to get 16.

$$16a^{4}$$

Differentiate w.r.t. a

$$64a^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{4}\times 8)$$

Multiply 2 and 8 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}a}(16a^{4})$$

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

$$4\times 16a^{4-1}$$

Multiply 4 times 16.

$$64a^{4-1}$$

Subtract 1 from 4.

$$64a^{3}$$