What do dy / DX and Dy mean in high numbers and what are the differences What do you mean sometimes

What do dy / DX and Dy mean in high numbers and what are the differences What do you mean sometimes

Dy / DX is the derivative of y to x, and Dy is the differential of Y
The derivative of y to X is the differential of Y divided by the differential of X, so the derivative is the quotient of the differential, also known as the derivative. These two concepts are different
To find dy is to find the differential of Y. if you are not familiar with differential operation, you can find dy / DX = f '(x) first, and then multiply DX to the right
dy=f'(x)dx

Derivative formula of function Find the derivative formula of exponential function, power function, logarithmic function, trigonometric function and inverse trigonometric function. It should be complete. (including special)

Y = f (x) = C (C is constant), then f '(x) = 0
F (x) = x ^ n (n is not equal to 0) f '(x) = NX ^ (n-1) (x ^ n represents the nth power of x)
f(x)=sinx f'(x)=cosx
f(x)=cosx f'(x)=-sinx
f(x)=tanx f'(x)=sec^2x
F (x) = a ^ x f '(x) = a ^ xlna (a > 0 and a is not equal to 1, x > 0)
f(x)=e^x f'(x)=e^x
F (x) = logax f '(x) = 1 / xlna (a > 0 and a is not equal to 1, x > 0)
f(x)=lnx f'(x)=1/x (x>0)
f(x)=tanx f'(x)=1/cos^2 x
f(x)=cotx f'(x)=- 1/sin^2 x
f(x)=acrsin(x) f'(x)=1/√(1-x^2)
f(x)=acrcos(x) f'(x)=-1/√(1-x^2)
f(x)=acrtan(x) f'(x)=-1/(1+x^2)

Derivative formula of exponential function

y=a^x
Take logarithm on both sides at the same time:
lny=xlna
Derivative x on both sides at the same time:
==>y'/y=lna
==>y'=ylna=a^xlna

Use the definition of derivative to find the derivative of the following functions: f(X)=X^3

F "(x) = LIM (t tends to 0) [f (x + T) - f (x)] / T = LIM (t tends to 0) [(x + T) ^ 3-x ^ 3] / T = LIM (t tends to 0) [(x + t-x) ((x + T) ^ 2 + X (x + T) + x ^ 2] / T = LIM (t tends to 0) [(x + T) ^ 2 + X (x + T) + x ^ 2] = 3x ^ 2

Using the definition of derivative to find the derivative of function y = √ (x-1)

Using the definition of derivative
　　y' = [√(x-1)]'
　　　= lim(h→0)[√(x+h-1)-√(x-1)]/h
　　　= lim(h→0){1/[√(x+h-1)+√(x-1)]
　　　= 1/[2√(x-1)]

What is the derivative of e ^ - x Is the derivative of e ^ - x equal to - e ^ - x

Yeah
=e^(-x)*(-x)'
=-e^(-x)