The derivative of logarthmic functions: If y = ln x, then y' = 1/x and if y = logaa x, then y' = 1/[(log a) x]The derivative of an exponential function: If y = a x , y = ax log aDifferentiation of Trigonometric FunctionsHere are the derivatives of trigonometric functions....
1、先给x赋值tensor([0., 1., 2., 3.])；2、将x设置为自动微分 ；3、赋值y表达式，计算y的...
x = 2, f'(2)>0, x应该要变小，才会使得f(x)变小 x = 1.5, f'(1.5)>0, x还是应该...
Find the derivative of (x2 + 5x – 3)/ 3 x½.Solution:This looks hard, but it isn't. The trick is to simplify the expression first: do the division (divide each term on the numerator by 3x½.Doing this we obtain(1/3)x3/2 + (5/3)x½ - x-½ (using the laws of ...
Shape-safety is currently supported up to rank-2 tensors, i.e. matrices. Example The following example shows how to derive higher-order partials of a function z of type ℝ²→ℝ: val z = x * (-sin(x * y) + y) * 4 // Infix notation val `∂z∕∂x` = d(z) / d(...
All derivative formulas and techniques are to be used in the process of implicit differentiation as well. ☛Related Topics: Derivative Calculator Calculus Calculator Second Derivative Calculator Differentiation Implicit Differentiation Examples Example 1:Find dy/dx by implicit differentiation: 3x + 2y = ...
60 X Oil DIC N2 objective (N.A. = 1.4), at 3X zooms, 0.5 um Z-interval, and 1024 × 1024 pixels. Three-dimensional (3D) reconstructions were performed, and spine density was quantified using the Filament module of IMARIS software (Bitplane) as described previously [25,26]...
If we have some function of f(x) = xn where n is a integer. dxndx = n xn-1 Example Differentiate, x3, 4x3, 4x2-6x + 6 Answers: 3x2, 12x2, 8x - 6 Chain Rule Given f(x) which is a function of another function g(x). Then h(x)=f(g(x)). The derivative is given by...
Explicit differentiation is used when 'y' is isolated, whereas implicit differentiation can be used similar to the chain rule when 'y' is not isolated. Learn more about implicit differentiation through examples of formulas and graphs. Related to this Question ...
这里有介绍：Complex Step Differentiation 相比有限差分有更好的数值稳定性，相比自动微分也要省事一些。