The derivative problem of mathematics, what is the derivative is ax

The derivative of this function is loga x, then the function is the integral of loga x.

According to the partial integration formula: u dv=uv - v du, let u=loga x, v=x, and we get:

loga x dx = x·loga x - x dloga x, where dloga x = dx xlna

Proof: First rebase loga x:

dloga x=d(lnx/lna)

Multiply one dx up and down to get:

d(lnx·dx/lna·dx)

dlnx/dx)·(dx/lna)

i.e. (lnx).'·(dx/lna)

Therefore the original formula = dx xlna

Continue: loga x dx

x·loga x - x dloga x

x·loga x - x dx/xlna

x·loga x - 1/lna dx

x·loga x - x/lna + c

So the derivative of x·loga x - x lna + c is loga x

Validation: x·loga x - x lna + c).'

loga x + x/xlna - 1/lnaloga x

The derivative of a(a+1)*x(a+1) is equal to ax a

Indicates a multiplication sign.

Keep in mind the law of derivatives.

It's a division.

f（x）＝v/u

f′（x）＝（v′u-vu′）/u²

The formula for finding the derivative of fractions, the square of the denominator is divided into upper and lower intelligence, and the upper and lower are subtracted.

f(x)=（2+x）ln(1+x)-2x

This step is to first find the derivative of (2+x), which is found to be 1

f'(x)=1*ln(1+x)+（2+x）/(1+x)-2

A simple calculation is sufficient, and the answer to the head of the limb celery calendar is shown in the first life picture.

Derivative is an important fundamental concept in calculus. When the increment of the independent variable tends to zero, the limit of the quotient between the increment of the dependent variable and the increment of the independent variable. When there is a derivative of a function, Qiao Liang said that the function is derivable or differentiable.

The derivative of the sum of the root friend code is equal to the sum property of the derivative, and the original derivative = (1).'-2lnx)'

Secondly, according to the formula, the derivative of this masking constant is 0 and the derivative of lnx is 1 x, so the derivative of the original function is.

2/x.

Here's how to do it

<>If you have help, dig and reform!

The first thing to know is whether it is the derivative of (e x) or (e x).

First of all, the equation of f(x) is simplified to make it easier and the derivative process can be carried out.

The results obtained are not similar terms, so there is no need to simplify them.

Typing with a mobile phone, there may be some deformation, I will write the steps in the following **, if you don't understand any step, you can continue to ask.

<> solution: f(x)=lnx-x+1,f'(x) = 1 x when x 0, f'(x) 0, the function f(x) decreases monotonically.

When x 0, f'(x) 0, the function f(x) increases monotonically.

x=0, the derivative does not exist, and the point function is not derivative.

f(x) =lnx -x+1

Define the domain = (0, +infinity).

f'(x) =1/x -1

f'(x) =0

1/x -1 =0

x=1f''(x) =1/x^2

f''(1) =1 <0 (max)

Monotony. Increment =(0,-1].

Decreasing=[-1, +infinity).