Solve -3(x/x^2)=

$$- 3 ( \frac { x } { x ^ { 2 } } ) =$$

Evaluate

$$-\frac{3}{x}$$

Solution Steps

Rewrite x^{2} as xx. Cancel out x in both numerator and denominator.

$$-3\times \frac{1}{x}$$

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

$$\frac{-3}{x}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Rewrite x^{2} as xx. Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3\times \frac{1}{x})$$

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

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

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

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

Multiply -1 times -3.

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

Subtract 1 from -1.

$$3x^{-2}$$