y=sqrt(10^(5-x))

find y'

how would you go about doing this one?

im studying for my "mastery test" on monday and i have never seen anything raise to a number - x

could someone show me how to do this please?

thank you

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- Oct 22nd 2009, 10:00 PMmybrohshi5Hard Derivative.
y=sqrt(10^(5-x))

find y'

how would you go about doing this one?

im studying for my "mastery test" on monday and i have never seen anything raise to a number - x

could someone show me how to do this please?

thank you - Oct 22nd 2009, 10:02 PMChris L T521
- Oct 22nd 2009, 10:07 PMmybrohshi5
yeah i can. but i seem to get a different answer then the answer of my review sheet.

i get -10^(.5(5-x)) * ln(10)

but....

the answer on the sheet is -10^(.5(5-x)) / 2 - Oct 22nd 2009, 10:08 PMendling
Use logarithmic differentiation.

sqrt of 10^(5-x) is the same as 10^[(5-x)/2]

Take the natural log of both sides.

ln y = ln 10^[(5-x)/2]

ln y = [(5-x)/2] ln 10 because lnx^a = a lnx

then differentiate:

(1/y)(dy/dx) = (-1/2)ln10

solve for dy/dx:

dy/dx = (-1/2)(ln10)(10^[(5-x)/2])

edit: The answer sheet is wrong? :P - Oct 22nd 2009, 10:18 PMmybrohshi5
haha ok thank you very much =)