Derivation by first principles: cos(x^0.5)

  • Thread starter PedroB
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  • #1
PedroB
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Homework Statement



Find the derivative of the function f(x)=cos(√x) by first principles

Homework Equations



f'(x)= lim as h tends to zero of [f(x+h)-f(x)]/h

The Attempt at a Solution



Problems arise immediately, since I have no idea what to do with the expression cos(√(x+h)), I've tried binomial expansion, but to no avail. Any help would be greatly appreciated
 

Answers and Replies

  • #2
pasmith
Homework Helper
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Homework Statement



Find the derivative of the function f(x)=cos(√x) by first principles

Homework Equations



f'(x)= lim as h tends to zero of [f(x+h)-f(x)]/h

The Attempt at a Solution



Problems arise immediately, since I have no idea what to do with the expression cos(√(x+h)), I've tried binomial expansion, but to no avail. Any help would be greatly appreciated

[tex]
\cos(\sqrt{x + h}) = \cos(\sqrt{x}(1 + h/x)^{1/2})
[/tex]
and keep the first two terms of the binomial expansion of [itex](1 + h/x)^{1/2}[/itex].
 

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