What is the derivative of y=e^square root of 1+tan(sinx)?

Click For Summary
SUMMARY

The derivative of the function y=e^√(1+tan(sin(x))) can be computed using the chain rule. The correct application involves differentiating the outer function and then the inner functions sequentially. The derivative is expressed as y' = e^√(1+tan(sin(x))) * (1 + tan(sin(x)))'. The final result requires careful evaluation of each component, particularly the derivative of the square root and the tangent function.

PREREQUISITES
  • Understanding of the chain rule in calculus
  • Familiarity with derivatives of exponential functions
  • Knowledge of trigonometric derivatives, specifically tan(sin(x))
  • Ability to manipulate and simplify expressions involving square roots
NEXT STEPS
  • Practice applying the chain rule with complex functions
  • Review derivatives of composite functions, focusing on exponential and trigonometric combinations
  • Explore examples of differentiating functions involving square roots
  • Learn to use LaTeX for clearer mathematical expression formatting
USEFUL FOR

Students studying calculus, particularly those tackling derivatives involving composite functions and the chain rule. This discussion is beneficial for anyone needing to clarify their understanding of differentiation techniques.

susan__t
Messages
20
Reaction score
0
Chain rule difficulties, due tomorrow!

Homework Statement



Find the derivative of

y=e^square root of 1+tan(sinx)

Homework Equations



chain rule: F'(x)=f'(g(x)) * g'(x)

The Attempt at a Solution



I thought I had it and then while I was looking at other chain rules and started doubting my actual ability to sort out the chain rule...

y=e^square root of 1+tan(sinx)

y'=e^square root of 1+tan(sinx) *(1+tansinx)'

y'=e^square root of 1+tan(sinx)* (0 +sec2sinx +cosx)

Please help! My assignment is due tomorrow and I know there is something not quite right but I don't know why.
 
Physics news on Phys.org


how would you evaluate these operations if you wanted to get a number out of them? Remember to take the chain rule in reverse of this order. For example, [tex]\frac{d[(x^{4})^3]}{dx} = 3(x^{4})^{2}*4x^{3}dx[/tex]

ok LaTeX appears to be acting up. Basically you forgot to take the derivative of the square root *before* finding the derivative of what was inside it.
 


yikes I should probably work on my recopying skills. thank you very much!
 

Similar threads

Replies
2
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K