Solve 6a^5*5a^3

$$6 a ^ { 5 } \cdot 5 a ^ { 3 }$$

Evaluate

$$30a^{8}$$

Solution Steps

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

$$6a^{8}\times 5$$

Multiply 6 and 5 to get 30.

$$30a^{8}$$

Differentiate w.r.t. a

$$240a^{7}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{8}\times 5)$$

Multiply 6 and 5 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}a}(30a^{8})$$

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

$$8\times 30a^{8-1}$$

Multiply 8 times 30.

$$240a^{8-1}$$

Subtract 1 from 8.

$$240a^{7}$$