Y = x (secx) ^ 2-tanx, the derivative of Y is? Please be as detailed as possible

Y = x (secx) ^ 2-tanx, the derivative of Y is? Please be as detailed as possible

y=(secx)^2+x*[(secx)^2]'-tanx'
y=(secx)^2-2x*tanx*(secx)^2-(secx)^2
y=-2x*tanx*(secx)^2

Derivation of (tanx-1) / secx

F (SiNx) = cos2x, find f (cos15 °)

f(sinx)=cos2x=1-2（sinx）^2
That is, f (x) = 1-2x ^ 2
F (cos15 °) = 1-2 (cos15 °) ^ 2 = 1-2 * (1 + cos30) / 2 = - radical 3 / 2

If f (cosx) = 3-cos2x, then f (SiNx) =?
Explain why!

∵ f (SiNx) = 3-cos2x = 3 - (1-2sinx * SiNx) ∵ f (x) = 3 - (1-2x * x) = 2 + 2x * x or: let SiNx = t cos2x = 1-2 (SiNx) ^ 2 = 1-2T ^ 2 F (SiNx) = 3-cos2x f (T) = 3 - (1-2T ^ 2) = 2T ^ 2 + 2 change t to x f (x) = 2x ^ 2 + 2 F (cosx) = 2cos ^ 2 x + 2 = 1 + cos2x + 2 = 3 + cos2x

Math story or knowledge less than 50 words

50 words of Mathematics
emergency

Arabic numerals
In life, we often use the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
These digital symbols were originally invented by ancient Indians, and later spread to Arabia and Europe from Arabia. Europeans mistakenly thought that they were invented by Arabs and called them "Arabic numerals". Up to now, people still mistakenly call these digital symbols issued by ancient Indians Arabic numerals

The origin of Mathematics

Mathematics, originated from the early production activities of human beings, is one of the Six Arts in ancient China, and also regarded as the starting point of philosophy by ancient Greek scholars. Its evolution can be seen as the continuous development of abstraction, or the extension of subject matter

Introduction to the origin and development of numbers
Don't copy. It's best to copy the original,

The ancient Greeks introduced the name, concept and self thinking into mathematics. They began to guess how mathematics came into being very early. Although their guess was only written down in a hurry, they almost occupied the thinking field of guess first

What is the origin of the Mid Autumn Festival
Not too long, within 100 words

The Mid Autumn Festival is a traditional festival in China. According to historical records, the word "Mid Autumn Festival" first appeared in the book of Zhou Li. In the Wei and Jin Dynasties, there was a record that "Yu Shang Shu Zhen Niu Cuo, mid autumn evening and around Weifu Pan Jiang". It was not until the early Tang Dynasty that the mid autumn festival became a fixed festival

The distance between the corresponding point of the complex number I / (1 + I) in the complex number plane and the origin is?

Write x + Yi distance as: (x ^ 2 + y ^ 2) ^ (1 / 2)
i/(1+i)
=i(1-i)/(1+i)(1-i)
=i-i^2)/(1-i^2)
=(i+1)/(1+1)
=1/2(1+i)=1/2+i/2
x=1/2 y=/12
S = 1 / 2 * (1 + 1) ^ (1 / 2) = radical 2 / 2