The chain rule for derivatives of a function of a function is extended to a function of a statistical functional, and applied to obtain approximations to the cumulants, distribution and quantiles of functions of sample moments, and so to obtain third order confidence intervals and estimates of red...
In differentiating this function, trying to use the power rule might result in a false statement as one could assume: ddxh(x)=3(x2)2=3x4 However, a quick check by using the laws of exponents reveals that h(x)=(x2)3=x6⟹ddxh(x)=6x5≠3x4 One more idea worth noticing is that ...
If w=f(x,y) is differentiable and if x=x(t), y=y(t) are differentiable functions of t, then the composite w=f(x(t),y(t)) is a differentiable function of t and dwdt=∂f∂xdxdt+∂f∂ydydt. 2. 三个中间变量+一个独立变量 Fig. 4 Khan Academy的独门绝技:五颜六色 这种...
Chain ruleGeneralizationMulti-layersThe expected supremum of a Gaussian process indexed by the image of an index set under a function class is bounded in terms of separate properties of the index set and the function class. The bound is relevant to the estimation of nonlinear transformations or ...
Answer and Explanation: We have to use the Chain Rule to find the derivative of the function. {eq}\displaystyle y = (2x^2 - 3)^3 {/eq} Differentiate the given function...Become a member and unlock all Study Answers Start today. Try it now Create an account Ask...
Chain Rule: The chain rule is a differentiation rule that allows us to determine the derivative of a composite function. To differentiate the composite functionb(g(x)), we can use: ddxb(g(x))=b′(g(x))g′(x) If an...
First, note that as a function of t, z is a function of a single variable. In this example, we have: Δ z / Δ x = y Δ z / Δ y = x dx/dt = 4t3 dy/dt = 6t Apply the chain rule formula from above to get the change in revenue over time: ...
The chain rule lets us "zoom into" a function and see how an initial change (x) can effect the final result down the line (g).Interpretation 1: Convert the ratesA common interpretation is to multiply the rates:x wiggles f. This creates a rate of change of dfdx, which wiggles g by ...
In English, the Chain Rule reads:The derivative of a composite function at a point, is equal to the derivative of the inner function at that point, times the derivative of the outer function at its image.As simple as it might be, the fact that the derivative of a composite function can...
A composite function is the combination of two (or more) functions. The chain rule allows us to find the derivative of a composite function. The chain rule can be generalised to multivariate functions, and represented by a tree diagram. The chain rule is applied extensively by the backpropagat...