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

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

Evaluate

$$6a^{4}$$

Solution Steps

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

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

Multiply 2 and -3 to get -6.

$$-6a^{2}\left(-a^{2}\right)$$

Multiply -6 and -1 to get 6.

$$6a^{2}a^{2}$$

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

$$6a^{4}$$

Differentiate w.r.t. a

$$24a^{3}$$

Steps Using Definition of a Derivative

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

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

Multiply 2 and -3 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-6a^{2}\left(-a^{2}\right))$$

Multiply -6 and -1 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{2}a^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{4})$$

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

$$4\times 6a^{4-1}$$

Multiply 4 times 6.

$$24a^{4-1}$$

Subtract 1 from 4.

$$24a^{3}$$