Help with Derivatives of f(g(h(x))) - I'm Stuck!

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Homework Help Overview

The discussion revolves around finding the derivative of the function f(x) = sqrt(sin(e^(x^4*sinx))). The original poster expresses frustration with their attempts to derive the function, particularly when treating it as a composition of functions f(g(h(x))).

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of the chain rule and product rule in the differentiation process. There are queries about specific parts of the derivative, particularly a "blue part" that seems to be missing or misunderstood. Some participants question the correctness of the original poster's expressions and suggest that the product rule needs to be applied correctly.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the steps involved in finding the derivative. There is acknowledgment of mistakes in the expressions provided, and some guidance is offered regarding the application of differentiation rules. However, there is no explicit consensus on the correct approach or solution yet.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the amount of direct assistance they can provide. There is a focus on understanding the differentiation process rather than simply obtaining the final answer.

hawkblader
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Homework Statement



Let f(x) = sqrt(sin(e^(x^4*sinx)))

Find f '(x)

I tried this many times and it's really frustrating!

I made it a composition function : f(g(h(x)))

but I'm not getting the answer at all.

At the end, I found :
1/2(sin(e^((x^4)(sinx))))^(-1/2) (cos(e^(x^4 sinx))) (e^(x^4 sinx)) (4x^3 cosx)

But it's wrong.

Could someone please tell me where I went wrong or how to solve this please.
 
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hawkblader said:
1/2(sin(e^((x^4)(sinx))))^(-1/2) (cos(e^(x^4 sinx))) (e^(x^4 sinx)) (4x^3 cosx+4*3x^2 sinx)

You left out the blue part.

ehild
 
Could you please tell me how you got the blue part?

I put it in and it's still wrong :(
 
hawkblader said:
Could you please tell me how you got the blue part?

I put it in and it's still wrong :(
Product rule.
 
hawkblader said:
1/2(sin(e^((x^4)(sinx))))^(-1/2) (cos(e^(x^4 sinx))) (e^(x^4 sinx)) (4x^3 cosx)

Sorry, I also was mistaken, the red part is wrong, as you have to apply the product rule on x4sinx.

ehild
 

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