What are the mathematical derivative formulas of 1
1.y=c(c is a constant) 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 = Tanks Y' =1/cos 2x
8.y=cotx y'=- 1/sin^2x
9 . y = arcsinx y'= 1/√ 1-x^2
10 . y = arc cosx y'=- 1/√ 1-x^2
1 1 . y = arctanx y'= 1/ 1+x^2
12 . y = arccotx y'=- 1/ 1+x^2
1 Several Methods of Derivation in Mathematics
Definition method: use the definition of derivative to find the derivative.
Formula method: find the derivative according to the formula given in the textbook.
Implicit function method: use implicit function to derive, and an example of implicit function derivation is given in the figure.
Logarithmic method: derivative by logarithm.
Compound function method: use compound function to get derivative.
Algorithm of 1 derivative
Derivative algorithm is four algorithms to guide the addition, subtraction, multiplication and division of numbers, and it is also an important content to master. The formula is as follows:
①(u v)=u'v vu '
②uv=u'v+uv '
③u/v=(u'v-uv')/v^2
Generally, u.v here are two different functions, and they are not constant at the same time. Among these three algorithms, it is particularly important to remember the derivation of the quotient of two functions. There is a negative sign in the molecule, which is easy to make mistakes. For the quadratic function mentioned above, it conforms to the sum and difference arithmetic of the function, so y' = (ax 2)'+(bx)'+c' = 2ax+b+0 = 2ax+b. 。