First, the derivation algorithm

Constant factor rule: if f(x) is a function and c is a constant, then d/dx(cf(x)) = c(d/dx(f(x)).

Addition and subtraction: if f(x) and g(x) are two functions, then d/dx (f (x)+g (x)) = d/dx (f (x)+d/dx (g (x)), d/dx (f (x)-g (x).

Multiplication rule: if f(x) and g(x) are two functions, then d/dx (f (x) g (x)) = f (x) d/dx (g (x))+g (x) d/dx (f (x)).

Division rule: if f(x) and g(x) are two functions, then d/dx (f (x)/g (x)) = [g (x) d/dx (f (x))-f (x) d/dx (g (x)] [g (x)

Second, the derivative formula

The derivative of a constant function is 0, that is, d/dx(c) = 0, where c is a constant.

The derivative of the power function is NX (n- 1), that is, d/dx (x n) = NX (n- 1), where n is a positive integer.

The derivative of exponential function is e x, that is, d/dx (e x) = e x.

The derivative of logarithmic function is 1/x, that is, d/dx (lnx) =1/x.

Third, the derivative of trigonometric function is:

The derivative of sinx is cosx, that is, d/dx (sinx) = cosx;

The derivative of cosx is -sinx, that is, d/dx (cosx) =-sinx;

The derivative of tanx is sec 2x, that is, d/dx (tanx) = sec2x;

The derivative of cotx is -CSC 2x, that is, d/dx (cotx) =-CSC 2x.

Four, the derivative of the inverse trigonometric function is:

The derivative of arcsinx is1√ (1-x 2), that is, d/dx (Arcsinx) =1√ (1-x 2);

The derivative of arccosx is-1√ (1-x 2), that is, d/dx (arccosx) =-1√ (1-x 2);

The derivative of arctanx is1/(1+x 2), that is, d/dx (arctanx) =1/(1+x 2).