The derivative is SiNx ^ 2 * cosx primitive function

The derivative is SiNx ^ 2 * cosx primitive function

(SiNx ^ 2) * cosx, because sin'x = cosx;
Then the original function is (SiNx ^ 3) / 3

1. Find the derivative of y = ln (x + 1). 2. Find the derivative of e ^ 2x
Let t = x + 1, then the derivative is 1 / (x + 1)
Let t = 2x, then the derivative is e ^ 2x
Why is 1 right and 2 wrong

The second question is wrong because you don't understand the derivation of composite function. I suggest you take a look at the derivation of composite function
Let t = 2x f (x) = e ^ 2x = e ^ t
f'(x) =f'(t)*t‘（x)
=(e^t)*2
In this case, we change t back to X and get f '(x) = 2E ^ (2x)

Finding the derivative of y = x-ln (2e ^ x + 1 + √ (e ^ 2x + 4E ^ x + 1))
How to do it

y=1-1/(2e^x+1+√(e^2x+4e^x+1))*(2e^x+1/2*((e^2x+4e^x+1))^(-1/2)*(2e^(2x)+4e^x)))

Finding the derivative of 1 / ln (x + 1)

The derivative of 1 / ln (x + 1)
=-1/(ln(x+1))²* (ln(x+1))'
=-1/(ln(x+1))²* (1/(x+1))
=-1/[(x+1)(ln(x+1))²]

Given the function f (x) = x & # 178; + 1 / 2 x = 0, if f (1) + F (a) = 2, then the real number a=
Given the function f (x) = x & # 178; + 1 / 2 x = 0, if f (1) + F (a) = 2, then the real number a=

F (x) = x & # 178; + 1 / 2, X

It is known that for the X function f (x) = (1-A) x2 + (a + 2) x-4, a is a real number. Find: (1) the function f (x) has only one zero point in [- 2,1], find the value range of a; (2) all zeros of function f (x) are greater than 0, find the value range of A

(1) ∵ function has only one zero point in [- 2,1], ∵ f (- 2) × f (1) ≤ 0 (2 points) (when the equal sign is different), that is: - 1 (- 6a-4) ≤ 0, the solution is: a ≤ − 23, that is, the value range of a is (- ∞, - 23]. & nbsp (5 points) (2) when 1-A = 0, that is, a = 1, then 3x-4 = 0

For all real numbers x satisfying | x ≠ 1, the function f (x) satisfies f (x-3 / x + 1) + F (3 + X / 1-x) = x, and all possible values of F (x) are obtained

8!

If the function f (x) = X-1 / x + A is odd, then the value of real number a is zero

F (x) = X-1 / x + A is an odd function
f(x)+f(-x)
=x-1/x+a+(-x)-1/(-x)+a
=2a
=0
a=0

I want to know the formula of PI
Letter representation

PI, generally expressed in π, is a mathematical constant that exists in mathematics and physics. It is defined as the ratio of circumference to diameter of a circle. It is also equal to the ratio of area to square radius of a circle. It is the key value to accurately calculate the circumference, area and volume of a circle
In analysis, π can be strictly defined as the minimum positive real number x satisfying sin (x) = 0, where sin is a sine function (using the definition of analysis)

Area formula of PI

S=π*R²
S = (?) 189; LR L is the arc length
S = (?) 189; α R (?) 178; angle in radian