Qeustion 2 The Bessel function of order 0, y= J(x), satisfies the differential equation xy" + y' + xy = 0, (1) for all values of x and its value at 0 is J(0) = 1. 1. Find J'(0). [Hint: Take x = 1 in the equation (1).] Use implicit differentiation to find J"(0). [Hint: Take derivative for the equation (1).] 2.

use implicit differentiation to calculate higher derivatives.

Find dy/dx by implicit differentiation. x6 + y³ = 23 Step 1 With implicit differentiation, we differentiate all the terms in our equation with respect to x. Keep in mind we are implying that y is a function of x. Think of it as y(x). In order to differentiate it, we will need to use the Chain Rule. To start, differentiate both sides of the equation with respect to x. x6 + y³ = 23 d_[y³] dx 6 x -[x6] + dx 5 + d_[y³] dx = = [23] dx Step 2 Use the Chain Rule to find the derivative of y³. If it helps, think of y as y(x). dy [³] = dx