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Differentiate w.r.t. z
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\frac{\mathrm{d}}{\mathrm{d}z}(-z^{4})
Combine 7z^{4} and -8z^{4} to get -z^{4}.
4\left(-1\right)z^{4-1}
The derivative of ax^{n} is nax^{n-1}.
-4z^{4-1}
Multiply 4 times -1.
-4z^{3}
Subtract 1 from 4.
-z^{4}
Combine 7z^{4} and -8z^{4} to get -z^{4}.