1, (sinx)'=cosx, that is, the derivative of sine is cosine.

(cosx)'=-sinx, that is, the derivative of cosine is the reciprocal of sine.

(tanx)' = (secx) 2, that is, the derivative of the tangent is the square of the secant.

(cotx)' =-(cscx) 2, that is, the derivative of cotangent is the reciprocal of the square of cotangent.

5.(secx)'=secxtanx, that is, the derivative of secant is the product of secant and tangent.

6.(cscx)'=-cscxcotx, that is, the derivative of cotangent is the inverse of cotangent and cotangent product.

7、(arctanx)'= 1/( 1+x^2)。

8、(arccotx)'=- 1/( 1+x^2)。

9, (fg)'=f'g+fg', that is, the derivative of the product is equal to the product of the derivative of each factor and other functions, and then sum.

10, (f/g)' = (f' g-fg')/g 2, that is, the derivative of the quotient. Take the square of the division function as the division formula. The difference between the product of the derivative of divisor function and the product of divisor function minus the product of the derivative of divisor function is the divisor.

1 1, (f (-1) (x))' =1/f' (y), that is, the derivative of the inverse function is the reciprocal of the derivative of the original function. Pay attention to the transformation of variables.

Precautions for derivative products

For the derivation of a function, it is generally necessary to follow the principle of simplifying first and then deriving. When seeking derivative, we should not only pay attention to the application of derivative law, but also pay special attention to the restrictive effect of derivative law on derivative. When simplifying, we should first pay attention to the equivalence of transformation and avoid unnecessary operational errors.

We need to remember several common high-order derivative formulas, convert other functions into our common functions, and just substitute them into formulas. By finding the first derivative, the second derivative and the third derivative, we can find out the relationship between them.