MTH 425 Lecture Notes - Lecture 2: Elul, Bundesautobahn 45, Ethylene

6. Find the orthogonal trajectories of the family of curves. 7. T/F (with justification) The differential equation yz y is separable.

Find the derivative of the function. y = 4xe-kx y'(x) = 4e-kx -4ke-kx Please try again using a combination of the Product Rule and the Chain Rule. First apply the Product Rule. In order to find the derivatives of the separate terms, use the Chain Rule by identifying the outer and inner functions f'(x) and g(x) such that you can rewrite the expression as y = f(g(x)). Use the Chain Rule formula which states d/dxf(g(x)) = f'(g(x)).g'(x).