Solve {z}^frac{1{4}}{left(z/right)}^-frac{1{2}}

$${ z }^{ \frac{ 1 }{ 4 } } { \left( \frac{ z }{ } \right) }^{ - \frac{ 1 }{ 2 } }$$

Differentiate w.r.t. z

$$-\frac{1}{4z^{\frac{5}{4}}}$$

Steps Using Definition of a Derivative

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{\frac{1}{4}}z^{-\frac{1}{2}})$$

To multiply powers of the same base, add their exponents. Add \frac{1}{4} and -\frac{1}{2} to get -\frac{1}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{-\frac{1}{4}})$$

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

$$-\frac{1}{4}z^{-\frac{1}{4}-1}$$

Subtract 1 from -\frac{1}{4}.

$$-\frac{1}{4}z^{-\frac{5}{4}}$$

Evaluate

$$\frac{1}{\sqrt[4]{z}}$$