Question

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

Answer 1

I tried this:

Explanation:

Here you need to evaluate three differential starting from the exponential (leaving the exponent as it is) and multiply by the derivative of the `csc` again leaving the argument as it is and finally times the differential of the root.

I tried using colours to discriminate between the three differentials:

`(df(x))/(dx)=color(red)(e^(csc(sqrt(x)))color(blue)((-csc(sqrt(x))cot(sqrt(x))))color(green)(1/(2sqrt(x))`