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

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

Evaluate

$$\frac{11a^{2}}{3}$$

Solution Steps

The opposite of -\frac{2}{3}a^{2} is \frac{2}{3}a^{2}.

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

Combine 3a^{2} and \frac{2}{3}a^{2} to get \frac{11}{3}a^{2}.

$$\frac{11}{3}a^{2}$$

Differentiate w.r.t. a

$$\frac{22a}{3}$$

Steps Using Definition of a Derivative

The opposite of -\frac{2}{3}a^{2} is \frac{2}{3}a^{2}.

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

Combine 3a^{2} and \frac{2}{3}a^{2} to get \frac{11}{3}a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{11}{3}a^{2})$$

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

$$2\times \frac{11}{3}a^{2-1}$$

Multiply 2 times \frac{11}{3}.

$$\frac{22}{3}a^{2-1}$$

Subtract 1 from 2.

$$\frac{22}{3}a^{1}$$

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

$$\frac{22}{3}a$$