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Math Help - calculus urgent help

  1. #1
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    calculus urgent help

    Just a couple of questions i need some help with:

    1. find the first and second derivative of: e^sin(x)
    2. A rectangle's lower vertices are on the x-axis and upper vertices on the graph of y = sinx(x) for (0 is less than or equal to x which is less than or equal to pi). Find the expression for the area of the rectangle and the maximum area of the rectangle.

    3. for the function cos(x) + sin(x)
    a. (i) show that f(-π/4) = 0
    (ii) find in terms of pi, the smallest positive value of x which satisfies f(x) = 0.

    4. For e^(x)(cosx +sinx) window: -2 < x < 3.
    a. find the first derivative
    b. the maximum point
    c. the second derivative

    5. Find the first derivative of (sinxc)^2 cosx
    a. show that the maximum point is x = the square root of 1/3
    b. find the exact maximum value
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by samantha_malone View Post
    1. find the first and second derivative of: e^sin(x)
    Are you familiar with the chain rule and product rule?

    f(x)=e^{u}
    f'(x)=u'e^u
    f'(x)=u''e^u+(u')^2e^u
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