一、链式法则Chain rule【1】 开始推导反向传播原理之前,先了解一下链式法则: Case1 取y=g(x),z=h(y)。 当改变x时,x 会通过 g 影响 y;而当改变 y 时,y 会通过 h 影响 z。 因此,如果要计算 dz/dx,由于这种效应,可以计算Derivative:dz/dy 乘 dy/dx。 Case2 取x=g(s),y=g(s)。 然后有一...
The Chain Rule in Differential Calculus. Equation of the Tangent Line with the Chain Rule. Formulas and Examples.
How would we calculate the derivative in these cases? The following theorem gives us the answer for the case of one independent variable.theorem: Chain rule for one independent variable Suppose that x=g(t)x=g(t) and y=h(t)y=h(t) are differentiable functions of tt and z=f(x,y)z=...
(sinx)2. The chain rule states that thederivativeDof a composite function is given by a product, asD(f(g(x))) =Df(g(x)) ∙Dg(x). In other words, the first factor on the right,Df(g(x)), indicates that the derivative off(x) is first found as usual, and thenx, wherever it...
The Chain Rule says: the derivative of f(g(x)) = f’(g(x))g’(x) The individual derivatives are: f'(g) = −1/(g2) g'(x) = −sin(x) So: (1/cos(x))’ = −1g(x)2(−sin(x)) = sin(x)cos2(x) Note: sin(x)cos2(x) is also tan(x)cos(x) or many othe...
Example 4. Assume that y is a function of x. y = y(x). Apply the chain rule to d dx y2 .Solution. dy2 dx = dy2 dy · dydx = 2y dy dx .y, which we are assuming to be a function of x, is inside the function y2. The derivative of y2with respect to y is 2y. As ...
Try applying the product rule to: ddx(dfdxdxdt) The notation ddx(something) means "the value at x of the derivative of the function that takes x to (something)". But "the function that takes x to (f∘x)′(t)x′(t)" is ill defined. Edit: I should have said f′(x(t))x′...
Chain Rule for Derivative — The Theory https://ift.tt/2YDoEwS About 0 Minutes In calculus, Chain Rule is a powerful differentiation rule for handling the derivative of composite functions. While its mechanics appears relatively straight-...
注意到计算 \frac{\partial z}{\partial t} 时只需固定 s ,计算 z 关于t 的导数(ordinary derivative)即可;计算 \frac{\partial z}{\partial s} 时思路类似. 则可将此时的链式法则视作第1.种情况下的拓展. 3. 设 u 为关于 n 个变量 x_1, x2,……, xn 的可微函数且各个 xj( j=1,2,…,n...
Chain rulegravitational time dilationrotating platformThis paper has a pedagogical aim. Indeed, by using the relativistic velocity-addition and Einstein's equivalence principle (EEP), we want to analyse in a simple way the physics of time on a rotating non-inertial frame. We use a didactic ...