Help me send me a derivative formula for a function and a derivative formula for a special function,

Derivatives of basic functions.

c'=0 (c is constant).

x^n)'=nx^(n-1) (n∈r)

sinx)'=cosx

cosx)'=-sinx

e^x)'=e^x

a^x)'=(a x)*lna(a>0 and a≠1)logax)].'= 1 (x·lna)(a>0 and a≠1 and x>0)lnx].'= 1/x

and the derivative of the differential product quotient function.

f(x) +g(x)]' = f'(x) +g'(x)f(x) -g(x)]' = f'(x) -g'(x)f(x)g(x)]' = f'(x)g(x) +f(x)g'(x)f(x)/g(x)]' = [f'(x)g(x) -f(x)g'(x)] / [g(x)^2]

Derivative of a composite function.

Let y=u(t) and t=v(x), then y'(x) = u'(t)v'(x) = u'[v(x)] v'(x)

Example: y = t 2 , t = sinx, then y'(x) = 2t * cosx = 2sinx*cosx = sin2x

Derivative is an important basic concept in calculus, and derivative is essentially a process of finding the limit, and the common derivative formula is y=c (c is a constant) y'=0y=x^ny'=nx^(n-1)y=a^xy'=a^xlna，y=e^xy'=e^x、y=logaxy'=logae/x，y=lnxy'=1/x。

Trigonometric functions (also called"Circular functions") is a function of angles; They are important in studying triangles and modeling periodic phenomena and many other applications. Trigonometric function is usually defined as the ratio of the two sides of a right triangle containing this angle, and can also be defined equivalently as the length of various line segments on a unit circle. More modern definitions express them as infinite series or solutions to specific differential equations, allowing them to extend to arbitrary positive and negative values, even complex values.

From the 5th century to the 12th century AD, Indian mathematicians made great contributions to trigonometry. Although trigonometry was still a computational tool of astronomy at that time, it was greatly enriched by the efforts of Indian mathematicians.

The concepts of "sine" and "cosine" in trigonometry were first introduced by Indian mathematicians, who created a more accurate sine table than Ptolemy's.

c'=0 (c is a constant function); x^n)'= nx^(n-1) (n∈q)； sinx)' = cosx； ④cosx)' = - sinx； ⑤e^x)' = e^x； ⑥a^x)'= a xlna (ln is the natural logarithm of inx).'= 1 x (ln is the natural logarithm logax).'=(xlna) (1), (a>0 and a is not equal to 1).

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The answer is as follows: tan( x 4)-1).'Say goodbye.

tan(πx/4)）'

SEC sock blade ( x 4) * (4).

/4)sec²(πx/4)

Write (x - 1 x)ln(2x 1) and then use the derivative formula of the product, f'(x)＝(1＋1/x²)ln(2x＋1)

2(x - 1/x)/(2x＋1)

It is seen as the derivative of the quotient of the numerator as the product of two functions.