Solve -1/-32dx/x

$$\frac { - 1 } { - 3 } \frac { 2 d x } { x }$$

Evaluate

$$\frac{2d}{3}$$

Solution Steps

Fraction \frac{-1}{-3} can be simplified to \frac{1}{3} by removing the negative sign from both the numerator and the denominator.

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

Cancel out x in both numerator and denominator.

$$\frac{1}{3}\times 2d$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{2}{3}d$$

Differentiate w.r.t. d

$$\frac{2}{3} = 0.6666666666666666$$

Steps Using Definition of a Derivative

Fraction \frac{-1}{-3} can be simplified to \frac{1}{3} by removing the negative sign from both the numerator and the denominator.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{3}\times \frac{2dx}{x})$$

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{3}\times 2d)$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

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

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

$$\frac{2}{3}d^{1-1}$$

Subtract 1 from 1.

$$\frac{2}{3}d^{0}$$

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

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

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

$$\frac{2}{3}$$