常见基本函数的导数

1  常见基本函数的导数

大部分复杂函数都可以由简单函数组合而成,工科生小书架为大家列出基本函数的导数:

基本函数导数
y = xndy/dx = n xn-1
y = a xndy/dx = a n xn-1
f(x) = a xnf'(x) = a n xn-1
y = exdy/dx = ex
y = ea xdy/dx = a ea x
y = axdy/dx = ax ln(a)
y = ln(x)dy/dx = 1 / x
y = sin(Θ)dy/dΘ = cos(Θ)
y = cos(Θ)dy/dΘ = – sin(Θ)
y = tan(Θ)dy/dΘ = sec2(Θ)
y = cot(Θ)dy/dΘ = cosec2(Θ)
y = sec(Θ)dy/dΘ = tan(Θ) sec(Θ)= sin(Θ) / cos2(Θ)
y = cosec(Θ)dy/dΘ = – cot(Θ) cosec(Θ)= – cos(Θ) / sin2(Θ)
y = sin-1(x / a)dy/dx = 1 / (a2 – x2)1/2
y = cos-1(x / a)dy/dx = – 1 / (a2 – x2)1/2
y = tan-1(x / a)dy/dx = a / (a2 + x2)
y = cot-1(x / a)dy/dx = – a / (a2 + x2)
y = sec-1(x / a)dy/dx = a / (x (x2 – a2)1/2)
y = cosec-1(x / a)dy/dx = – a / (x (x2 – a2)1/2)

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