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

Answer 1

I tried this:

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))#
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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