Question

How do you differentiate `e^((2-sqrtx)^2)` using the chain rule?

Answer 1

`y' = e^((2 - sqrt(x))^2) - (2e^((2 - sqrt(x))^2))/sqrt(x)`

Explanation:

This function can be simplified to `e^(4 - 4sqrt(x) + x)`.

We now use the rule that if `y = e^(f(x)),` then `y' = f'(x) xx e^(f(x))`.

So, letting `y = e^square`, with `square = 4 - 4sqrt(x) + x`, we will have to find the derivative of `square`.

`square' = 1 - (0 xx 4sqrt(x) + 1/(2x^(1/2)) xx -4) =1 -2/(x^(1/2))`

So, the derivative is `y' = (1- 2/sqrt(x)) e^((2 -sqrt(x))^2) = e^((2 - sqrt(x))^2) - (2e^((2 - sqrt(x))^2))/sqrt(x)`

Hopefully this helps!