Y=c(c is a constant) y'=0. y=x^n,y'=nx^(n- 1)。 y=a^x,y'=a^xlna。 y=e^x,y'=e^x。 y=logax，y'=logae/x .y=lnx，y'= 1/x .y=sinx，y'=cosx .y=cosx，y'=-sinx .y=tanx,y'= 1/cos^2x。 y=cotx,y'=- 1/sin^2x。 y=arcsinx,y'= 1/√ 1-x^2。 y=arctanx,y'= 1/ 1+x^2。

The difference between derivative and partial derivative;

The difference between derivative and partial derivative is different in definition, geometric meaning and solution.

1, the limit of the ratio of the change of function value to the change of independent variable. Unary function, one y corresponds to one x, and the derivative is only one. A binary function, where a z corresponds to an x and a y, has two derivatives, one is the derivative of z to x, and the other is the derivative of z to y, which is called partial derivative.

2. Partial derivative means that a function contains several variables and only one of them is derived, z=x+y, which means that the function of z contains two variables, x and y.

The derivative of any one of them is called partial derivative. Direct derivative means that a function has only one variable, so it can be derived. Find the increment of function δy = f(x0+δx)-f(x0), find the average rate of change, find the limit and find the derivative.

Extended data:

Derivation is a calculation method in mathematical calculation, and its definition is the limit of the quotient between the increment of dependent variable and the increment of independent variable when the increment of independent variable tends to zero.

Derivative is defined as the limit of the quotient between the increment of dependent variable and the increment of independent variable when the increment of independent variable tends to zero. When a function has a derivative, it is said that the function is derivable or differentiable. The differentiable function must be continuous. Discontinuous functions must be nondifferentiable.

Some important concepts in physics, geometry, economics and other disciplines can be expressed by derivatives. For example, derivatives can represent the instantaneous speed and acceleration of a moving object, the slope of a curve at a point, the margin and elasticity in economics.