Solve -2/3*x*3/2

$$- \frac { 2 } { 3 } \cdot x \cdot \frac { 3 } { 2 }$$

Evaluate

$$-x$$

Solution Steps

Multiply -\frac{2}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\times 3}{3\times 2}x$$

Cancel out 3 in both numerator and denominator.

$$\frac{-2}{2}x$$

Divide -2 by 2 to get -1.

$$-x$$

Differentiate w.r.t. x

$$-1$$

Steps Using Definition of a Derivative

Multiply -\frac{2}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2}{2}x)$$

Divide -2 by 2 to get -1.

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

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

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

Subtract 1 from 1.

$$-x^{0}$$

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

$$-1$$