Solve 3x^2*1/x

$$3 x ^ { 2 } \times \frac { 1 } { x }$$

Evaluate

$$3x$$

Solution Steps

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

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

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

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

Cancel out x in both numerator and denominator.

$$3x$$

Differentiate w.r.t. x

$$3$$

Steps Using Definition of a Derivative

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

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

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

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

Cancel out x in both numerator and denominator.

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

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

$$3x^{1-1}$$

Subtract 1 from 1.

$$3x^{0}$$

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

$$3\times 1$$

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

$$3$$