Solve 0.3a(-2a)*3.overline{3}

$$0.3 a ( - 2 a ) \cdot 3 . \overline { 3 }$$

Evaluate

$$-\frac{9a^{2}}{5}$$

Solution Steps

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

$$0.3a^{2}\left(-2\right)\times 3$$

Multiply 0.3 and -2 to get -0.6.

$$-0.6a^{2}\times 3$$

Multiply -0.6 and 3 to get -1.8.

$$-1.8a^{2}$$

Differentiate w.r.t. a

$$-\frac{18a}{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(0.3a^{2}\left(-2\right)\times 3)$$

Multiply 0.3 and -2 to get -0.6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-0.6a^{2}\times 3)$$

Multiply -0.6 and 3 to get -1.8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-1.8a^{2})$$

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

$$2\left(-1.8\right)a^{2-1}$$

Multiply 2 times -1.8.

$$-3.6a^{2-1}$$

Subtract 1 from 2.

$$-3.6a^{1}$$

For any term t, t^{1}=t.

$$-3.6a$$