Solve 2gamma^2/(gamma^2)^(frac{3{2)}}

$$\frac { 2 \gamma ^ { 2 } } { ( \gamma ^ { 2 } ) ^ { ( \frac { 3 } { 2 } ) } }$$

Evaluate

$$\frac{2\gamma ^{2}}{\left(|\gamma |\right)^{3}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and \frac{3}{2} to get 3.

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

Cancel out \gamma ^{2} in both numerator and denominator.

$$\frac{2}{\gamma }$$

Differentiate w.r.t. γ

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

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and \frac{3}{2} to get 3.

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

Cancel out \gamma ^{2} in both numerator and denominator.

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

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

$$-2\gamma ^{-1-1}$$

Subtract 1 from -1.

$$-2\gamma ^{-2}$$