从导数的定义证明,导数的定义就是由y(x+△x)趋近到y(x)在增量△x趋近于0时的趋近率,核心知识点就是求极限值,直线时候即是斜率值.
则y'=lim△x→0[(y(x+△x))-y(x))/(x+△x-x)]=lim△x→0[((x+△x)n-xn)/△x]=nxn-1.(分子用Cknxk△x(n-k)拆开,很简单证明之).
如何证明gradient of any tangent to the curve y=x^n
1个回答
相关问题
-
Find an equation of the tangent line to the curve at the giv
-
find the equation of the normal to the curve y=3x2-2x-1which
-
an equation of the line tangent to the graph of f(x)=x(1-2x)
-
For what value of A is the plane 2x-2y+z=3 is tangent to the
-
find the area under the curve of y=|x|between x=-1 and x=1
-
数学问题~The line y = 2x + k is a tangent to the circle x2 + y2
-
英语翻译suppose that the slope of the tangent line to the graph
-
(x^n)*(y^n)=(x*y)^n 这个公式叫什么?如何证明它?
-
Way to wreck the curve.
-
The region enclosed by the curves y=x^2,and x=y^2 is rotated