What is the derivative of E to the 2x power

2e 2x analysis:

Remember the basic derivative formula (e x).'=e^x。

So here we get the derivative (e 2x).'=e^2x*(2x)'=2e^2x。

Memorize the basic derivative formula.

e^x)'=e^x

So here's the derivation.

e^2x)'=e^2x *(2x)'=2e^2x

Derivative of e to the 2x power: 2e (2x).

e (2x) is a composite function consisting of u=2x and y=e u.

The calculation steps are as follows:

1. Let u=2x and find the derivative u of u about x'=2。

2. Derivative u to the power of e, the result is the power of e, and the value of u is e (2x).

3. Multiply the derivative of e by the u power of e by the derivative of u with respect to x to find the result, and the result is 2e (2x).

Any non-zero number to the power of 0 is equal to 1. Here's why:

Usually represents to the power of 3.

The 3rd power of 5 is 125, i.e. 5 5 5 = 125.

The 2nd power of 5 is 25, i.e. 5 5 = 25.

The power of 5 to the power of 5 is 5, i.e. 5 1 = 5.

It can be seen that when n 0, the (n+1) power of 5 becomes the nth power of 5 needs to be divided by a 5, so the power of 5 can be defined as: 5 5 = 1.

y=e^(x^2)。Take the logarithm of both sides to get lny=x 2.

The derivatives of x on both sides give y y=2x.

y`=y*2x。

2x*e^(x^2)。

Derivative of Derivative:

The derivative of a function consisting of the sum, difference, product, quotient, or composite of the fundamental function can be derived from the derivative of the function. The basic derivative is as follows:

1. Linearity of derivation: Derivation of linear combination of functions is equivalent to finding the derivative of each part of the function and then taking the linear combination (i.e., formula).

2. The derivative function of the product of two functions: one derivative multiplied by two + one by two derivative (i.e. formula).

3. The derivative function of the quotient of two functions is also a fraction: (sub-derivative mother-child multiplication mother) divided by the female square (i.e., formula).

4. If there is a composite function, the derivative is obtained by the chain rule.

The derivative of the 2x order of e is: 2e 2x.

Derivative, also known as derivative value, also known as microquotient, is an important basic concept in calculus and is a local property of functions.

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 derivable function must be continuous; Discontinuous functions must not be derivative.

If the function y=f(x) is derivable at every point in the open interval, the function f(x) is said to be derivable in the interval. At this time, the function y=f(x) corresponds to a definite derivative value for each definite x value in the interval, which constitutes a new function, which is called the derivative of the original function y=f(x), denoted as y'、f'(x), dy dx, or df(x) dx, referred to as the derivative.

Derivatives are an important pillar of calculus. Newton and Leibniz contributed to this. The function y=f(x) is the derivative f at the point x0'Geometric meaning of (x0):

Represents the slope of the tangent of the function curve at the point p0(x0,f(x0)) (the geometric meaning of the derivative is the tangent slope of the function curve at this point).

The derivative of x to the power of x is: y = e (x 2).

Take the logarithm of both sides to get lny=x 2.

The derivatives of x on both sides give y y=2x.

y`=y*2x

2x*e^(x^2)。

Derivative is an important fundamental concept in calculus. When the independent variable x of the function y=f(x) produces an incremental δx at a point x0, the ratio of the incremental δy of the output value of the function to the incremental δx of the independent variable is at the limit a when δx approaches 0 if it exists, a is the derivative at x0 and is denoted as f'(x0) or df(x0) dx.

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 both the independent variables and the values of the function are real, the derivative of the function at a point is the tangent slope of the curve represented by the function at that point.

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.

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