Question

How do you differentiate `f(x)=e^(cossqrtx)` using the chain rule.?

Answer 1

`e^cos(sqrt(x)) xx (-sin(sqrt(x))) xx 1/(2sqrt(x))`

Explanation:

Understand this that this is in the form of `f(g(h(x)))` where `f(x) = e^x`, `g(x)=cos(x)` and `h(x) = sqrt(x)`

First, you need to know these things

`d/dx(e^x)=e^x`
`d/dx(cos(x))=-sin(x)`
`d/dx(sqrt(x))=1/(2sqrt(x))`

So, this becomes

Derivative = `e^cos(sqrt(x)) xx (-sin(sqrt(x))) xx 1/(2sqrt(x))`