Solve 2a^5*3a^3

$$2 a ^ { 5 } \times 3 a ^ { 3 }$$

Evaluate

$$6a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$2a^{8}\times 3$$

Multiply 2 and 3 to get 6.

$$6a^{8}$$

Differentiate w.r.t. a

$$48a^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{8}\times 3)$$

Multiply 2 and 3 to get 6.

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

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

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

Multiply 8 times 6.

$$48a^{8-1}$$

Subtract 1 from 8.

$$48a^{7}$$