00:03
For part a of the given problem, we need to evaluate a formula for double derivative of the given function f of g of x.
00:21
By chain rule, we can write the first derivative as f -dash -of -g -of -x into g -dash -of -x.
00:38
In order to find the double derivative, we will have.
00:42
To apply product rule first so double derivative can be denoted by y double dash applying product rule we get d by d x of f dash of g of x into g dash of x plus d by d x of f dash of g of x in order to find the derivative of this expression, we will have to apply chain rule, which we can do in the next step.
01:26
So for now, we can write d by d x of f dash of g of x into g dash of x plus g double dash of x into f dash of g of x.
01:46
For this expression over here, we assume that the inner function is g of x and the outer function y is f -dash -of -u.
02:02
Thus, d -u by d -x can be written as g -dash -of -x, and d -y by d -x can be written as f -double -dash -u, which can be written as f -double dash of x.
02:19
Hence our equation for the double derivative can be written as g -dash -of -x whole square into f -double -dash -of -g -of -x plus g -double -x into f -double -dash -of -x into f -dash -g of g of x...