Solve -3/2[x^-3/-3]

$$- \frac { 3 } { 2 } [ \frac { x ^ { - 3 } } { - 3 } ]$$

Evaluate

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

Solution Steps

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

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

Cancel out 3 in both numerator and denominator.

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

Cancel out -1 in both numerator and denominator.

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

Differentiate w.r.t. x

$$-\frac{3}{2x^{4}}$$

Steps Using Definition of a Derivative

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

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

Cancel out 3 in both numerator and denominator.

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

Cancel out -1 in both numerator and denominator.

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

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

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

Multiply -3 times \frac{1}{2}.

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

Subtract 1 from -3.

$$-\frac{3}{2}x^{-4}$$