Find the first order partial derivative: f(x,y)= x^3+4x^2y-2xy^3 Compute the first-order partial derivative of f (x, y) = 3 x^2 + x^3 y + 4 y^2. Compute all first-order partial derivative of the: F(u,v) = 20u (ln(5vu)) ...
The second derivative with respect to x of the three-dimensional Gaussian-like function is written as, ∂ 2 G ∂x 2 = (4x 2 −2)e −(x 2 +y 2 +z 2 ) . (13) Using Theorem 1 where N = 2, we need 6 basis functions. Tables 1, 2 and 3 were arrived at by using the...
Example 2: Finding the 4th Derivative of a Trigonometric Function Let's take a look at the following function: $$y=sin(2x) $$ We're trying to find the 4th derivative, so we are looking to find {eq}\frac{\mathrm{d^{4}} y}{\mathrm{d} x^{4}} {/eq}. ...
To solve the given problem, we need to find the determinant of the matrix formed by y and its derivatives up to the 8th order, where y=sin(px) and yn is the nth derivative of y. 1. Define the function and its derivatives: - Let y=sin(px). - The derivatives of y can be comput...
This polynomial is an approximation to the function. Answer and Explanation: To find the Taylor series expansion we need to find the derivative of the function. The Taylor series of a function about a point a is given by {eq...