Solve (-5a^2)*3a^3=

$$( - 5 a ^ { 2 } ) \cdot 3 a ^ { 3 } =$$

Evaluate

$$-15a^{5}$$

Solution Steps

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

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

Multiply -5 and 3 to get -15.

$$-15a^{5}$$

Differentiate w.r.t. a

$$-75a^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(-5a^{5}\times 3)$$

Multiply -5 and 3 to get -15.

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

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

$$5\left(-15\right)a^{5-1}$$

Multiply 5 times -15.

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

Subtract 1 from 5.

$$-75a^{4}$$