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

You haven't written this topic clearly!