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Calculus

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F(x) = x^2 sin x
F'(x)

y= tan x/x^2
y'=

  • Calculus - ,

    F = x^2 sinx
    use the product rule to get
    F' = 2x sinx + x^2 cosx

    F = tanx/x^2
    use quotient rule to get
    F' = (x^2 sec^2 x - 2x tanx)/x^4
    = (x sec^2 x - 2tanx)/x^3

    or, writing F as
    F = x^-2 tanx
    use the product rule to get
    F' = -2x^-3 tanx + x^-2 sec^2 x
    = x^-3 (-2tanx + x sec^2 x)

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