Trig derivatives? f(x)=7arcsin(x^2)
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Trig derivatives? f(x)=7arcsin(x^2)

[From: ] [author: ] [Date: 11-09-30] [Hit: ]
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If f(x)= 7arcsin(x^2) what is the derivative? f'(x)

please help

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derivative of arcsin(u) = u'/sqrt(1-u^2)
here u = x^2.

[7 arcsin(x^2)]' = 7*[arcsin(x^2)]' = 7*[2x/(sqrt(1-(x^2)^2))] = 14x/(sqrt(1-x^4)).

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Let y = f(x)= 7arcsin(x^2) f')x) = dy/dx or
x^2 = sin (y/7) ----------------------------------------… 1or
2x = (1/7)cos(y/7)*(dy/dx)
or f'(x)=dy/dx = (14x)/cos(y/7) = 14x/sq rt[1-sin^2(y/7)] = 14x/[√(1-x^4)] from 1
1
keywords: Trig,arcsin,derivatives,Trig derivatives? f(x)=7arcsin(x^2)
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