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Evaluate
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Differentiate w.r.t. z
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\frac{z^{-4}}{2z^{-9}}
Cancel out 2^{6} in both numerator and denominator.
\frac{z^{5}}{2}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}z}(\frac{z^{-4}}{2z^{-9}})
Cancel out 2^{6} in both numerator and denominator.
\frac{\mathrm{d}}{\mathrm{d}z}(\frac{z^{5}}{2})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
5\times \frac{1}{2}z^{5-1}
The derivative of ax^{n} is nax^{n-1}.
\frac{5}{2}z^{5-1}
Multiply 5 times \frac{1}{2}.
\frac{5}{2}z^{4}
Subtract 1 from 5.