What is the Derivative of 1-e^2x?

  • Context: Undergrad 
  • Thread starter Thread starter erjkism
  • Start date Start date
  • Tags Tags
    Derivative
Click For Summary
SUMMARY

The derivative of the function 1 - e^(2x) is calculated using the chain rule. By letting u = 2x, the derivative u' is determined to be 2. The function can be expressed as y = 1 - e^u, leading to the derivative y' = -e^u * u', which simplifies to y' = -2e^(2x).

PREREQUISITES
  • Understanding of calculus concepts, specifically derivatives
  • Familiarity with the chain rule in differentiation
  • Knowledge of exponential functions and their properties
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the chain rule in calculus for deeper comprehension
  • Explore exponential functions and their derivatives
  • Practice calculating derivatives of composite functions
  • Learn about higher-order derivatives and their applications
USEFUL FOR

Students studying calculus, mathematics educators, and anyone looking to strengthen their understanding of differentiation techniques.

erjkism
Messages
54
Reaction score
0
derivative of 1-e^2x?

does anyone know how to do this one?

derivative of 1-e^2x?
 
Physics news on Phys.org
All that's needed is the chain rule.

Let u = 2x, then u' = 2

y = 1-eu

y' = -euu' = -2e2x
 

Similar threads

Undergrad Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How Can Nested Summation Functions Be Simplified or Reversed?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Taking the derivative of a function
  • · Replies 15 ·
Replies
15
Views
3K
High School Second Derivative Question -- Help Understanding the Importance Please
  • · Replies 13 ·
Replies
13
Views
3K
MHB Finding k for x is undefined at $x=2$
  • · Replies 3 ·
Replies
3
Views
1K
High School Confusion on Implicit Differentiation
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad Question about Inverse Derivative Hyperbola function
  • · Replies 2 ·
Replies
2
Views
1K
MHB (e^ix)-1=(2ie^(ix/2))x(sin (x/2))
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Finding the derivative of a characteristic function
  • · Replies 5 ·
Replies
5
Views
3K
Maclaurin Series When 0 is in the Denominator?
  • · Replies 48 ·
2
Replies
48
Views
5K