151x Filetype PDF File size 0.04 MB Source: www.sfu.ca
Kenyon College paquind@kenyon.edu Math 333 Some Practice with Partial Derivatives Suppose that f(t,y) is a function of both t and y. The partial derivative of f with respect to y, written ∂f, ∂y is the derivative of f with respect to y with t held constant. To find ∂f, you should ∂y consider t as a constant and then find the derivative of f with respect to y. 2 3 Example. Suppose f(t,y) = t sin(y ). Then ∂f 2 3 2 ∂y =t cos(y )·3y . Some Practice Problems. 3 2 ∂f 1. Suppose f(t,y) = t y . Find ∂y. t+y ∂f 2. Suppose f(t,y) = e . Find ∂y. 2 ∂f 3. Suppose f(t,y) = ln(t y). Find ∂y. 4. Suppose f(t,y) = cos(ty). Find ∂f. ∂y 5. Suppose f(t,y) = ty . Find ∂f. 3 2 sin(t +y ) ∂y Answers to the Practice Problems. ∂f 3 1. ∂y = 2t y ∂f t+y 2. ∂y = e ∂f 1 2 3. = 2 ·t ∂y t y 4. ∂f = −sin(ty)·(t) ∂y 3 2 5. ∂f = t−cos(t +y )2y ∂y 2 3 2 sin (t +y ) Math 333: Diff Eq 1 Partial Derivatives
no reviews yet
Please Login to review.