(1) Find the derivative of the function y=f(x) at x0:
① Find the increment δ y = f (x0+δ x)-f (x0) of the function.
② Find the average change rate.
③ Seek the limit and derivative.
(2) Derivative formulas of several common functions:
① C'=0(C is a constant);
②(x^n)'=nx^(n- 1)(n∈q)；
③(sinx)' = cosx；
④(cosx)' =-sinx；
⑤(e^x)'=e^x；
⑥ (a x)' = a A Xin (ln is natural logarithm).
⑦ loga(x)'=( 1/x)loga(e)
(3) Four algorithms of derivative:
①(u v)'=u' v '
②(uv)'=u'v+uv '
③(u/v)'=(u'v-uv')/ v^2
④[u(v)]'=[u'(v)]*v' (u(v) is a compound function f[g(x)])
(4) Derivative of compound function: the derivative of compound function to independent variable is equal to the derivative of known function to intermediate variable, multiplied by the derivative of intermediate variable to independent variable-called chain rule.
Extended data:
Derivation is the foundation of calculus and an important pillar of calculus calculation. Some important concepts in physics, geometry, economics and other disciplines can be expressed by derivatives. For example, derivatives can represent the instantaneous speed and acceleration of a moving object, the slope of a curve at a certain point, and the margin and elasticity in economics.
A term in mathematics, that is, to derive a function, with
Express delivery.
Inverse function derivation rule:
Ruo function
Strictly monotone differentiable, its inverse function
Derivative of existence sum
.
Derivation rules of composite functions;
if
It can be guided at point X.
It can also be derived at the corresponding point u, and its composite function
Is derivable at point X.
.
Derivation rule of implicit function:
if
There is an implicit function in.
Here, it is only said that y is a function of x, not that y must be solved explicitly. that is
Although y has no inverse solution, as long as the implicit function of y about x exists and is derivable, we can still find its inverse function by using the derivative rule of composite function.
References:
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