Solve 5a^2*6a^4

$$5 a ^ { 2 } \cdot 6 a ^ { 4 }$$

Evaluate

$$30a^{6}$$

Solution Steps

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

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

Multiply 5 and 6 to get 30.

$$30a^{6}$$

Differentiate w.r.t. a

$$180a^{5}$$

Steps Using Definition of a Derivative

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

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

Multiply 5 and 6 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}a}(30a^{6})$$

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

$$6\times 30a^{6-1}$$

Multiply 6 times 30.

$$180a^{6-1}$$

Subtract 1 from 6.

$$180a^{5}$$