高等数学中常用的求导公式

1. 常数函数导数：d/dx(c) = 0

2. 幂函数导数：d/dx(x^a) = a*x^(a-1)

3. 指数函数导数：d/dx(e^x) = e^x

4. 对数函数导数：d/dx(ln(x)) = 1/x

5. 反三角函数导数：d/dx(arcsin(x)) = 1/√(1-x^2), d/dx(arccos(x)) = -1/√(1-x^2), d/dx(arctan(x)) = 1/(1+x^2)

6. 三角函数导数：d/dx(sin(x)) = cos(x), d/dx(cos(x)) = -sin(x), d/dx(tan(x)) = sec^2(x)

7. 反双曲函数导数：d/dx(arcsinh(x)) = 1/√(x^2+1), d/dx(arccosh(x)) = 1/√(x^2-1), d/dx(arctanh(x)) = 1/(1-x^2)

8. 双曲函数导数：d/dx(sinh(x)) = cosh(x), d/dx(cosh(x)) = sinh(x), d/dx(tanh(x)) = sech^2(x)

9. 常数倍规则：d/dx(c*f(x)) = c*d/dx(f(x))

10. 加法法则：d/dx(f(x) + g(x)) = d/dx(f(x)) + d/dx(g(x))

11. 减法法则：d/dx(f(x) - g(x)) = d/dx(f(x)) - d/dx(g(x))

12. 乘法法则：d/dx(f(x) * g(x)) = f(x)*d/dx(g(x)) + g(x)*d/dx(f(x))

13. 除法法则：d/dx(f(x) / g(x)) = (g(x)*d/dx(f(x)) - f(x)*d/dx(g(x))) / (g(x))^2

14. 反函数法则：d/dx(f^(-1)(x)) = 1 / (d/dx(f(x)))

15. 链式法则：d/dx(f(g(x))) = d/dx(f(g(x))) * d/dx(g(x))

16. 幂函数逆导数：d/dx(x^(1/a)) = (1/a) * x^(1/a - 1)

17. 指数函数逆导数：d/dx(ln(x)) = 1/x

18. 对数函数逆导数：d/dx(e^x) = e^x

19. 反三角函数逆导数：d/dx(sin^(-1)(x)) = 1/√(1-x^2), d/dx(cos^(-1)(x)) = -1/√(1-x^2), d/dx(tan^(-1)(x)) = 1/(1+x^2)

20. 倒数法则：d/dx(1/f(x)) = - (1/f(x)^2) * d/dx(f(x))

21. 乘法逆法则：d/dx(f(x)/g(x)) = (g(x)*d/dx(f(x)) - f(x)*d/dx(g(x))) / (g(x))^2

22. 复合函数导数：d/dx(f(g(x))) = d(f)/d(g) * d(g)/d(x)

23. 向量函数求导：d/dx(f(x)) = (d/dx(f1(x)), d/dx(f2(x)), ..., d/dx(fn(x)))

24. 链式法则的高阶导数：(d^n)/(dx^n)(f(g(x))) = (d^n)/(dg^n)(f(g(x))) * (d^n)/(dx^n)(g(x))