Calculus

If f(x)= sqrt(4sin(x)+2), then f'(0)=

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asked by Anna
  1. Use the substitution
    u=4sin(x)+2
    f'(x)=df(x)/dx
    =df(u)/du * du/dx
    =d(sqrt(u))/du * d(4sin(x)+2)/dx
    =1/(2sqrt(u)) * 4cos(x)
    =2cos(x)/sqrt(4sin(x)+2))

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    posted by MathMate
  2. Well the Sqrt(4sin(x)+2) is the same thing as saying (4sin(x)+2)^(1/2)....sooo take the derivative using the chain rule. So first you would take the derivative of the outside by bringing the (1/2) and subtracting one from the exponent. Then take the derivative of the inside. 4 is a constant so it remains the same since it being multiplied. Sin(x)has the derivative cos(x) and since the two is a constant its derivative is zero. Your answer should look like this:
    (4cos(x))/(2sqrt(4sin(x)+2)

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    posted by Nisa
  3. radical 2

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    posted by Tiffany

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