求导公式运算法则

2025-03-16 08:47:08
推荐回答(2个)
回答1:

运算法则是:加(减)法则,[f(x)+g(x)]'=f(x)'+g(x)';乘法法则,[f(x)*g(x)]'=f(x)'*g(x)+g(x)'*f(x);除法法则,[f(x)/g(x)]'=[f(x)'*g(x)-g(x)'*f(x)]/g(x)^2。若某函数在某一点导数存在,则称其在这一点可导,否则称为不可导。
导数也叫导函数值,又名微商,是微积分中的重要基础概念。由基本函数的和、差、积、商或相互复合构成的函数的导函数则可以通过函数的求导法则来推导。
求导运算法则是:加(减)法则:[f(x)+g(x)]'=f(x)'+g(x)';乘法法则:[f(x)*g(x)]'=f(x)'*g(x)+g(x)'*f(x);除法法则:[f(x)/g(x)]'=[f(x)'*g(x)-g(x)'*f(x)]/g(x)^2。
不是所有的函数都有导数,一个函数也不一定在所有的点上都有导数。若某函数在某一点导数存在,则称其在这一点可导,否则称为不可导。然而,可导的函数一定连续;不连续的函数一定不可导。

回答2:

运算法则

减法法则:(f(x)-g(x))'=f'(x)-g'(x)

加法法则:(f(x)+g(x))'=f'(x)+g'(x)

乘法法则:(f(x)g(x))'=f'(x)g(x)+f(x)g'(x)

除法法则:(g(x)/f(x))'=(g'(x)f(x)-f'(x)g(x))/(f(x))^2

导数公式

1.y=c(c为常数) y'=0

2.y=x^n y'=nx^(n-1)

3.y=a^x y'=a^xlna

y=e^x y'=e^x

4.y=logax y'=logae/x

y=lnx y'=1/x

5.y=sinx y'=cosx

6.y=cosx y'=-sinx

7.y=tanx y'=1/cos^2x

8.y=cotx y'=-1/sin^2x

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