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Differentiate the algebraic expression \[R(z)=\frac{6}{\sqrt{z^{3}}}+\frac{1}{8 z^{4}}-\frac{1}{3 z^{10}}\]
in Mathematics by Diamond (58,497 points) | 29 views

1 Answer

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Best answer
Remember that you'll need to rewrite the terms so that each of the \(z\) 's are in the numerator with negative exponents and rewrite the root as a fractional exponent before taking the derivative. Here is the rewritten function.
\[
R(z)=6 z^{-\frac{3}{2}}+\frac{1}{8} z^{-4}-\frac{1}{3} z^{-10}
\]
The derivative is,
\[
R^{\prime}(z)=6\left(-\frac{3}{2}\right) z^{-\frac{5}{2}}+\frac{1}{8}(-4) z^{-5}-\frac{1}{3}(-10) z^{-11}=-9 z^{-\frac{5}{2}}-\frac{1}{2} z^{-5}+\frac{10}{3} z^{-11}
\]
by Platinum (131,394 points)
Good work boss. Just want to confirm if it is always necessary to express the final answer as the question was. Like in this case, leaving it in radical form.

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