Math Problem Statement
Calculate the derivative of the following function.
yequals=tangent left parenthesis e Superscript x Baseline right parenthesistanex
Question content area bottom
Part 1
StartFraction dy Over dx EndFractiondydxequals=enter your response here
Solution
To calculate the derivative of the given function:
We will use the chain rule, which states that:
Here, and .
Step-by-step process:
-
Differentiate the outer function (tangent): The derivative of is . So, applying this to :
-
Differentiate the inner function (exponential): The derivative of is simply .
-
Apply the chain rule: Now, multiply the derivative of the outer function by the derivative of the inner function:
Thus, the derivative of is:
Would you like further details or have any questions about this?
Here are 5 related questions for further practice:
- What is the derivative of ?
- How do you differentiate ?
- What is the second derivative of ?
- How does the chain rule apply to differentiating trigonometric functions?
- What is the derivative of ?
Tip: Always remember the chain rule when you have a function composed of multiple functions!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Chain Rule
Trigonometric Functions
Formulas
Derivative of tan(x): sec^2(x)
Chain Rule: d/dx [f(g(x))] = f'(g(x)) * g'(x)
Theorems
Chain Rule
Derivative of Exponential Functions
Suitable Grade Level
Grades 11-12 / College Level