Solve (a)(-3a)(a^2)

$$( a ) ( - 3 a ) ( a ^ { 2 } )$$

Evaluate

$$-3a^{4}$$

Solution Steps

Multiply a and a to get a^{2}.

$$a^{2}\left(-3\right)a^{2}$$

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

$$a^{4}\left(-3\right)$$

Differentiate w.r.t. a

$$-12a^{3}$$

Steps Using Definition of a Derivative

Multiply a and a to get a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{2}\left(-3\right)a^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}\left(-3\right))$$

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

$$4\left(-3\right)a^{4-1}$$

Multiply 4 times -3.

$$-12a^{4-1}$$

Subtract 1 from 4.

$$-12a^{3}$$