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

  • Thread starter Thread starter hawkblader
  • Start date Start date
  • Tags Tags
    Derivatives
Click For Summary
SUMMARY

The discussion focuses on finding the derivative of the function f(x) = sqrt(sin(e^(x^4*sin(x)))). The user attempted to apply the chain rule and product rule but encountered errors in their calculations. The correct derivative involves applying the product rule to the term x^4*sin(x) and includes components such as (1/2)(sin(e^(x^4*sin(x))))^(-1/2) and (cos(e^(x^4*sin(x))))(e^(x^4*sin(x))). The key takeaway is the necessity of correctly applying differentiation rules to composite functions.

PREREQUISITES
  • Understanding of calculus, specifically differentiation techniques.
  • Familiarity with the chain rule and product rule in calculus.
  • Knowledge of trigonometric and exponential functions.
  • Ability to manipulate composite functions for differentiation.
NEXT STEPS
  • Review the chain rule and product rule in calculus.
  • Practice finding derivatives of composite functions with examples.
  • Explore the implications of the derivative in real-world applications.
  • Study common mistakes in differentiation to avoid similar errors.
USEFUL FOR

Students studying calculus, particularly those struggling with derivatives of composite functions, and educators looking for examples of common pitfalls in differentiation.

hawkblader
Messages
4
Reaction score
0

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.
 
Physics news on Phys.org
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
 

Similar threads

Derivative of a sinusoidal function
  • · Replies 2 ·
Replies
2
Views
2K
Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
  • · Replies 3 ·
Replies
3
Views
2K
Limit of 0^0: Evaluating x^sinx
  • · Replies 19 ·
Replies
19
Views
2K
How to Solve a Second Order Nonhomogeneous Differential Equation?
  • · Replies 9 ·
Replies
9
Views
2K
Find g(x)/h(y) for a given F(x,y)
  • · Replies 3 ·
Replies
3
Views
1K
How can I determine the potential extrema on a function with a discontinuity?
  • · Replies 4 ·
Replies
4
Views
1K
How should I use the averaging approximation to find this?
  • · Replies 3 ·
Replies
3
Views
2K
Differential Equations: Solve the following
  • · Replies 2 ·
Replies
2
Views
2K
Method of Undetermined Coefficients
  • · Replies 1 ·
Replies
1
Views
2K
Determining domain for C^1 function
  • · Replies 4 ·
Replies
4
Views
1K