calculus

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Find dy/dx, if y= 5e^x/cosx

  • calculus -

    y = (5e^x)/(cos x)
    Since 1/cos(x) = sec(x), we can also rewrite this as
    (5e^x)(sec(x))
    Since two terms which are both functions of x are multiplied, we use the chain rule. Thus it becomes:
    (5e^x)(sec(x)) + (5e^x)(tan(x) * sec(x))
    Simplifying,
    dy/dx = (5e^x)(sec(x))(1 + tan(x))

    Hope this helps~ :3

  • calculus -

    Let f(x) = e^x
    So f'(x) = e^x
    Let g(x) = cos(x)
    So g'(x) = -sin(x)

    Use:
    (f/g)' = ((f'×g)-(f×g'))/g^2

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