Solve 5a^2*15a^3

$$5 a ^ { 2 } \cdot 15 a ^ { 3 }$$

Evaluate

$$75a^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$5a^{5}\times 15$$

Multiply 5 and 15 to get 75.

$$75a^{5}$$

Differentiate w.r.t. a

$$375a^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5a^{5}\times 15)$$

Multiply 5 and 15 to get 75.

$$\frac{\mathrm{d}}{\mathrm{d}a}(75a^{5})$$

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

$$5\times 75a^{5-1}$$

Multiply 5 times 75.

$$375a^{5-1}$$

Subtract 1 from 5.

$$375a^{4}$$