Solve 3a^2(1/a)

$$3 a ^ { 2 } ( \frac { 1 } { a } )$$

Evaluate

$$3a$$

Solution Steps

Express 3\times \frac{1}{a} as a single fraction.

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

Express \frac{3}{a}a^{2} as a single fraction.

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

Cancel out a in both numerator and denominator.

$$3a$$

Differentiate w.r.t. a

$$3$$

Steps Using Definition of a Derivative

Express 3\times \frac{1}{a} as a single fraction.

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

Express \frac{3}{a}a^{2} as a single fraction.

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

Cancel out a in both numerator and denominator.

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

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

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

Subtract 1 from 1.

$$3a^{0}$$

For any term t except 0, t^{0}=1.

$$3\times 1$$

For any term t, t\times 1=t and 1t=t.

$$3$$