1, continuous function must be differentiable (×)
For example, the function y=|x| is a continuous non-derivative function.
2. trigonometric functions and inverse trigonometric functions are bounded functions (×)
The function y=tanx is an unbounded function.
3. Differentiable function is not integrable function (×)
Y=x, y= 1/x, y = x 2 are all differentiable functions and are all integrable.
4. All differentiable functions are nondifferentiable functions (×)
For univariate function, it is differentiable, and multivariate function does not hold.
Third, calculate the first derivative and differential of the following functions
1,y=cos2x/ln3x
y'=(-2sin2x*ln3x-cos2x/x)/(ln3x)^2
dy=y'dx=[(-2sin2x*ln3x-cos2x/x)/(ln3x)^2]dx
2、y=[arctan3x]^2
y'=6arctan3x/( 1+9x^2)
dy=y'dx=[6arctan3x/( 1+9x^2)]dx
3,dy=d[ln^(cscx+cotx)]
dy=d[ln^(cscx+cotx)]=-cscxdx
y'=dy/dx=-cscx
Fourth, calculate the second derivative of the following function
1,y= 1n√sinx
y'=cotx/2
y''=-csc^2x/2
The implicit function determined by v1n (x2+y2) = 2arcny/x, and find dy/dx.
Derivation of x on both sides
(2x+2yy')/(x^2+y^2)=2[(y'x-y)/x^2]/( 1+y^2/x^2)
Get y'=(x+y)/(x-y)
Six. Calculate the limits of the following functions
Lin (1-x) Tan
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① Characteristics of Montessori Sensory Training Teaching Aids
(1) isolation * * *
In Montessori teaching AIDS, each teaching aid only trains one kind of pe