second derivative dy dx

Conclusion - In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of dy/dx to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curve..

If the differential equation is of the form M dx + N dy = 0, then the condition for exactness is _____. => ∂ M ∂ y = ∂ N ∂ x or ∂ M ∂ y = ∂ N ∂ y or ∂ M ∂ y ≠ ∂ N ∂ x or ∂ M ∂ y + ∂ N ∂ x = 0 or &..

Solve the differential equation ( x + y 2 ) dx + (2 xy + 1) dy = 0. => IV or III or I or II or V..

Solve the differential equation (2 x + y + 1) dx + (2 y + x + 2) dy = 0. => IV or III or V or II or I..

Solve x (1 + y 2 ) dx + y (1 + x 2 ) dy = 0. => I or III or II or V or IV..

Choose the correct statement(s) for the differential equation M dx + N dy = 0, where M = ( x 2 + 2 x + y ) and N = ( x 2 + 4 y - 2). => III and V only or II only or I only or IV only or I and II only..

Solve the differential equation ( y 2 - 2 xy ) dx + (2 xy - x 2 ) dy = 0. => xy 2 - x 2 y 2 = c or xy 2 - x 2 y = c or xy 2 + x 2 y = c or xy 2 - xy..

dx and dy are called the differentials of x and y respectivel..

Second-order differential equations, by definition, contain a second derivative, like d 2 y/dx 2 , for example. As well as the second derivative, there may also be a first derivative in the equation and ..

x = a is called a point of inflexion. Rolle's theorem: If a function f(x) is such that (i) f (x) is continuous on [a,b] (ii) f (x) is differentiable on (a,b) and (iii) f (a) = f (b) Geometrical interpretation of Rolle's theorem Let AB be the graph of y = f(x) such that A = (a , f(a)) and ..