Solve 4a:6a^2=

$$4 a : 6 a ^ { 2 } =$$

Evaluate

$$\frac{2a^{3}}{3}$$

Solution Steps

Divide 4a by 6 to get \frac{2}{3}a.

$$\frac{2}{3}aa^{2}$$

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

$$\frac{2}{3}a^{3}$$

Differentiate w.r.t. a

$$2a^{2}$$

Steps Using Definition of a Derivative

Divide 4a by 6 to get \frac{2}{3}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2}{3}aa^{2})$$

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

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

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

$$3\times \frac{2}{3}a^{3-1}$$

Multiply 3 times \frac{2}{3}.

$$2a^{3-1}$$

Subtract 1 from 3.

$$2a^{2}$$