calculus

Basic formula of derivative:

(1)y=c(c is a constant), y' = 0；;

(2) y = x a (a is an arbitrary real number) and y' = ax (a-1);

(3)y=a^x(a>0,a≠ 1)、y′=a^xlna；

y=e^x，y′= e^x

(4)y=ln|x|，y′= 1/x；

(5)y=sinx，y′= cosx；

(6)y=cosx，y′=-sinx

(7)y=tanx，y′= sec？ x= 1/cos？ x

(8)y=ctgx，y′=-CSC？ x=- 1/sin？ x

Derivative of product, y=uv, y'=(uv)'=u'v+uv'

Derivative of quotient, y = u/v, y' = (u/v)' = (u' v-uv')/v? ,

Roberta's law-seeking the limit;

When f (x) and f (x) both tend to 0, or both tend to ∞, find lim[f(x)/F(x)], which belongs to 0/0 and ∞/∞ indefinite limits, and lim [f (x)/f (x)] = f' (x)/f.

Find the extreme value of the function f(x) at x0, and find the derivative f'(x) of f(x), and f'(x)=0.

indefinite integral

The operation of indefinite integral is the inverse operation of derivative.

∫f(x)dx=f(x)+C, where F(x) is called the integrand function and the derivative function of the original function, f(x)dx is called the integrand function expression, ∫ is called the integral symbol, and x is called the integral variable; "F(x)+C" is the result of integration, where c is a constant and F(x) is the original function of the integration result, so the key of indefinite integration is to find the original function from the derivative function, which is the inverse operation method of derivative method, but it is much more difficult than derivative.

F'(x)= f(x), and the key of integration is to find f(x) from f(x).

∫dF(x)=∫F′(x)dx =∫F(x)dx = F(x)+C .

Basic formula of indefinite integral:

( 1)∫0dx = C；

(2)∫dx = x+C；

(3)∫kdx = kx+C；

(4)∫x^adx=[ 1/(a+ 1)]x^(a+ 1)+c；

(5)∫e^xdx=e^x+c；

(6)∫a^xdx=( 1/lna)a^x+c,(a>0)；

(7)∫( 1/x)dx = ln | x |+C；

(8)∫cosxdx = sinx+C；

(9)∫sinxdx =-cosx+C；

(10)∫ seconds? dx = tanx+C；

( 1 1)∫cscxdx =-ctgx+C；

( 12)∫xsin xdx = sinx-xcos x+C；

( 13)∫xcosxdx=xsinx+cosx+C .

Both substitution integral method and partial integral formula should be familiar with.

There are many other formulas for high numbers. After getting started, you can learn and master them step by step according to different branches of mathematics. Step by step, you will learn well. I wish you success!