Why is there no derivative for y x?

y=|x|Derivatives at x≠0 and no derivatives at x=0 because f(x)= |x|The left derivative at x=0 is -1 and the right derivative is 1, and the two are not equal.

You can't say that there is a derivative of it.

It's just not at x=0, because it's not a smooth curve at this point.

The function has no derivative at x=0 and all other points are derivative. You can geometrically look at it, the derivative is the tangent slope of the curve at that point, so if the tangent exists, the derivative exists, and if the tangent does not exist, then the derivative does not exist either. Actually, this function doesn't have a tangent at 0, so it doesn't have a derivative.

This is intuitive, if strictly proven, the definition of the derivative can be used.

y=|x|=x (x>0)

y=|x|=0(x=0)

y=|x|=-x(x<0)

Gotta y'=1 x>0, y'=-1,x<0, since the left derivative at x=0 is -1 and the right derivative is 1, so y=|x|, which is not derivable at x=0.

y=1 x is defined in (negative infinity, 0) and (0, positive infinity), and it is discontinuous at 0, so there are derivatives in these two intervals, and it cannot be said that this function has no derivative because y=1 x is discontinuous at 0, and the existence of derivatives is for a certain interval;

y'=x^x*(lnx+1)。y=x xBecause there is no derivative formula for x x in the derivative formula of the basic function, it is necessary to do a transformation, and take the logarithm on both sides.

lny=lnx^x

lny=xlnx

Since y is a function of x, both sides find derivatives for x.

On the left, because y is a function of x, and Zen is based on a composite function.

Derivative, get y'/y

The right side is derived from x = x'*lnx+x*(lnx)'to get lnx+x xy'/y=lnx+x/x

y'=y*(lnx+1)

Because y=x x, substituting the above formula.

Get the derivative. y'=x^x*(lnx+1)

Commonly used formulas for the derivative of Elimination:

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^x4、y=logax y'=logae/x，y=lnx y'=1/x5、y=sinx y'=cosx

6、y=cosx y'=-sinx

7、y=tanx y'=1/cos^2x

8、y=cotx y'=-1/sin^2x9、y=arcsinx y'=1/√1-x^2

|y=|x|Actually, it actually isPiecewise functions，y=x(x>=0)y=-x(x=<0)。

Finding the derivatives separately shows that the derivative of y=x is y=1 and the derivative of y=-x is y=-1, that is, the two derivatives are not continuous at x=0, then the function is not derivable at x=0. Image of the excitation branch acre function.

is "smooth", there are no "sharp points". y=|x|, you can draw an image of it, it is a V-shape, and at x 0 is exactly the "sharp point" of the V, so it is not derivable.

It can be understood by the geometric definition:

Derivable, geometrically, means that the function image is "smooth" and there are no "cusps".

y=|x|, you can draw an image of it, it's a chevron, and at x 0 is exactly the "cusp" of the v, so it's not derivable.

Derivatives are local properties of functions. The derivative of a function at a point describes the rate of change of the function around that point. If the function is an argument.

If and are real values, the derivative of the function at a certain point is the tangent of the curve represented by the function at that point.

Slope. The essence of derivatives is to perform a local linear approximation of a function through the concept of limits. For example, in kinematics, the derivative of the displacement of an object with respect to time is the instantaneous velocity of the object.

Not all functions have derivatives, and a function does not necessarily have derivatives at all points. If a function exists at a certain point in derivative, it is said to be derivable at that point, otherwise it is called underivable. However, the function that can be used as a jujube guide must be continuous; Discontinuous functions must not be derivative.

The logarithm of both ends.

Get lny=x

lnx then derives x at both ends to get 1 y

y'=lnx+1

Sorted out'=y(lnx+1), replace the y on the right with the x power of x.

Get y'=x^x

lnx+1)

Calculation of derivativesCalculates derivatives of known functions.

It can be calculated using the limit of the ratio of change according to the definition of the derivative. In practice, most of the common analytic functions.

It can be regarded as the fruit of some simple functions with bridges, differences, products, quotients, or mutual overlapping and careful combinations.

As long as the derivatives of these simple functions are known, the derivatives of more complex functions can be deduced according to the derivative law of derivatives.

y=|x|Actually, it actually isPiecewise functions, y=x(x>=0)y=-x(x=<0), respectively, we will find that the derivative of y=x is y=1, and the derivative of y=-x is y=-1, that is, the two derivatives are discontinuous at x=0, then the function is not derivative at x=0.

It can be understood by the geometric definition:

Derivable, geometrically, refers to, a functional image.

is "smooth", there are no "sharp points".

y=|x|, you can draw an image of it, it's a chevron, and at x 0 is exactly the "cusp" of the v, so it's not derivable.

Derivable conditions of the function:

If a function defines a domain.

is the whole real number, i.e. the function is defined on it. A function needs certain conditions to be derivable at a point in the defined domain: the left and right derivatives of the function at the point of rent exist and are equal, and the derivatives of this point cannot be proved, only if the left and right derivatives exist and are equal and continuous at that point, can the point be derivable.

The derivable function must be continuous in the dismantling hole; A continuous function is not necessarily derivable, and a function that is discontinuous is not necessarily derivable.

Here's how, please refer to:

The question is not specific enough.

What is x+y equal, if it is a variable that is different from x and y, then a binary function is used.

Derivation. If it's an expression related to x and y, use an implicit function.

Derivative, if it is a constant, then a function of who is who (although the default is generally that y is a function of x).

Take the logarithm of the two ends to get lny=x

lnx then derives x at both ends to get 1 y

y'=lnx+1 to get y'=y(lnx+1) replaces the y on the right with the x power of x to get y'=x^x

lnx+1)。

Because: y=x

dy=dx x how to change, y to change, so the rate of change of the finger seepage is :

dy/dx=1

y=x straight line, past the origin (0,0), 45 degrees to the x-axis, tan45° 1 so only do the ridge: y' 1

Note that the domain x>0, y=x x, and take the logarithm of ln on both sides at the same time, and that lny=xlnx, and find the derivative of x on both sides, and note that y is a function of x'=xlnx)', i.e.: (1 y)y'=1+lnx, get y'=y(1+lnx)=(1+lnx)x x, that is, the desired molded plum fruit.