Math Problem Statement
Derivsigve of 2sec squared 5x plus 2x
Solution
To find the derivative of , we will use the following rules:
- The derivative of with respect to is .
- The chain rule: .
- The derivative of is simply .
Let's differentiate each term:
Step 1: Differentiate
First, apply the chain rule. The outer function is and the inner function is .
The derivative of is , so:
Step 2: Differentiate
The derivative of is simply .
Step 3: Combine both results
So the derivative of is:
Final Answer:
Would you like more details or have any questions?
Here are 5 related questions to expand your understanding:
- How would you differentiate ?
- What is the derivative of ?
- How does the chain rule apply to the function ?
- Can you find the second derivative of ?
- What are some applications of the derivative of in physics?
Tip: Always identify inner and outer functions clearly when using the chain rule for derivatives.
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Chain Rule
Trigonometric Functions
Formulas
Derivative of sec^2(u): 2 * sec^2(u) * tan(u)
Chain Rule: d/dx[f(g(x))] = f'(g(x)) * g'(x)
Derivative of a linear function: d/dx[2x] = 2
Theorems
Chain Rule
Derivative of Trigonometric Functions
Suitable Grade Level
Grades 11-12 / Early College