Difference between revisions of "009A Sample Midterm 3, Problem 5"

Revision as of 10:49, 3 November 2017

Find the derivatives of the following functions. Do not simplify.

(a) $f(x)=\sin {\bigg (}{\frac {x^{-3}}{e^{-x}}}{\bigg )}$

(b) $g(x)={\sqrt {\frac {x^{2}+2}{x^{2}+4}}}$

(c) $h(x)=(x+\cos ^{2}x)^{8}$

(insert picture of handwritten solution)

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 <span class="exam"> Find the derivatives of the following functions. Do not simplify.
-<span class="exam">(a)&nbsp; <math style="vertical-align: -16px">f(x)=\frac{(3x-5)(-x^{-2}+4x)}{x^{\frac{4}{5}}}</math>
+<span class="exam">(a)&nbsp; <math style="vertical-align: -16px">f(x)=\sin\bigg(\frac{x^{-3}}{e^{-x}}\bigg)</math>
-<span class="exam">(b)&nbsp; <math>g(x)=\sqrt{x}+\frac{1}{\sqrt{x}}+\sqrt{\pi}</math>&nbsp; for &nbsp;<math style="vertical-align: 0px">x>0.</math>
+<span class="exam">(b)&nbsp; <math style="vertical-align: -18px">g(x)=\sqrt{\frac{x^2+2}{x^2+4}}</math>
+<span class="exam">(c)&nbsp; <math style="vertical-align: -6px">h(x)=(x+\cos^2x)^8</math>
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