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

$$( a ^ { 2 } ) \times ( 2 a ^ { 2 } ) \times ( 4 a ^ { 3 } )$$

Evaluate

$$8a^{7}$$

Solution Steps

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

$$a^{4}\times 2\times 4a^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$a^{7}\times 2\times 4$$

Multiply 2 and 4 to get 8.

$$a^{7}\times 8$$

Differentiate w.r.t. a

$$56a^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}\times 2\times 4a^{3})$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{7}\times 2\times 4)$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{7}\times 8)$$

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

$$7\times 8a^{7-1}$$

Multiply 7 times 8.

$$56a^{7-1}$$

Subtract 1 from 7.

$$56a^{6}$$