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`(e^(x))/(sinx)`

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To differentiate the function \( y = \frac{e^x}{\sin x} \) with respect to \( x \), we will use the quotient rule. The quotient rule states that if you have a function in the form \( \frac{u}{v} \), then its derivative is given by: \[ \frac{dy}{dx} = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2} \] where \( u = e^x \) and \( v = \sin x \). ...
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Knowledge Check

  • If f(x) = (e^(x)-e^(sinx))/(2(x sinx)) , x != 0 is continuous at x = 0, then f(0) =

    A
    0
    B
    1
    C
    `1/2`
    D
    2

  • lim_(xrarr0)[(e^x-e^(sinx))/(x-sinx)] is equal to :

    A
    `-1`
    B
    0
    C
    1
    D
    none of these

  • lim_(xrarr0)[(e^x-e^(sinx))/(x-sinx)] is equal to

    A
    `-1`
    B
    0
    C
    1
    D
    None of these

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