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Mathematics 11 Online
OpenStudy (anonymous):

ap calc question. medal reward. question will be provided.

OpenStudy (anonymous):

find the derivative of \[\sec ^{-1}\sqrt{x}\]

hartnn (hartnn):

do you know chain rule ?

OpenStudy (anonymous):

yes

hartnn (hartnn):

derivative of sec x ?

hartnn (hartnn):

sorry derivative of sec inverse x ?

OpenStudy (anonymous):

yeah thats what i dont know.

OpenStudy (anonymous):

???

hartnn (hartnn):

\( \large \frac{d}{dz} sec^{-1} z = \frac{1}{z^2\,\sqrt{1 - z^{-2}}}; \quad z \neq -1, 0, +1 \)

OpenStudy (anonymous):

i thought it was\[\frac{ 1 }{ x \sqrt{x ^{2}-1} }\]

hartnn (hartnn):

its the same thing use the one you posted

OpenStudy (anonymous):

how do you incorporate the \[\sqrt{x}\]

hartnn (hartnn):

using chain rule , you multiply the derivative result by derivative of \(\sqrt x\)

OpenStudy (anonymous):

so \[\frac{ 1 }{ 2\sqrt{x}}\]

hartnn (hartnn):

\(\huge \dfrac{ 1 }{ \sqrt x \sqrt{x-1} }\times \dfrac{1}{2\sqrt x}\)

hartnn (hartnn):

and simplify

OpenStudy (anonymous):

alright thanks

hartnn (hartnn):

welcome ^_^

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