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....
Implicit differentiationis the process of differentiating animplicit function.An implicit function is a function that can be expressed as f(x, y) = 0. i.e., it cannot be easily solved for 'y' (or) it cannot be easily got into the form of y = f(x). Let us consider an example of...
我们尝试用它来求一个多项式f(x) = 3x^2+2x在x_0=2处的导数。通过手动计算f'(x)|_{x=2} =...
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 ...
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...
f(x)=(\ln(x))^2 Find the derivative using the Quotient Rule f(x) = \frac{x}{x+3} Differentiate the function. Simplify your answer. g(x) = (x^{3} - 1)^{3}(x^{3} + 1)^{3} Find and simplify the derivative of the following fun...
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 ...
f(x,y)=3x2y+xf(x,y)=3x2y+x ∂f∂x=6xy+1∂f∂x=6xy+1 在(x, y) = (1, 1) 时,f(x,y)=4.0f(x,y)=4.0, df/dx=7.0df/dx=7.0。 def f2d(x, y): ''' Args: :x: DNumber :y: DNumber :return: f(x, y) = 3*x**2*y + x and \partial f/\partial x '''...
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。