Solve -12a^2/3a=

$$\frac{ -12 { a }^{ 2 } }{ 3 } a=$$

Evaluate

$$-4a^{3}$$

Solution Steps

Divide -12a^{2} by 3 to get -4a^{2}.

$$-4a^{2}a$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-4a^{3}$$

Differentiate w.r.t. a

$$-12a^{2}$$

Steps Using Definition of a Derivative

Divide -12a^{2} by 3 to get -4a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-4a^{2}a)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

Multiply 3 times -4.

$$-12a^{3-1}$$

Subtract 1 from 3.

$$-12a^{2}$$