Math Problem Statement
(Secx cscx) /csc^2 - sec^2 find derivative
Solution
To find the derivative of the given expression , let's break it down step by step.
Step 1: Simplify the expression
Start by simplifying the first term:
So, the expression becomes:
Now, recall that:
Thus:
So the simplified expression is:
Step 2: Find the derivative
Now, let's differentiate the expression with respect to :
The derivative of is , and the derivative of is (using the chain rule).
So, the derivative is:
This is the derivative of the original expression.
Would you like more details on any of these steps? Here are some related questions:
- How do you differentiate and ?
- Can you simplify the expression further?
- What is the chain rule in differentiation?
- How does trigonometric identity play a role in differentiation?
- Can we find the derivative using an alternative method?
Tip: Always simplify the expression as much as possible before differentiating; this often makes the process easier.
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Math Problem Analysis
Mathematical Concepts
Calculus
Trigonometry
Differentiation
Formulas
Derivative of trigonometric functions: d/dx(tan(x)) = sec^2(x)
Simplification using trigonometric identities: sec(x) = 1/cos(x), csc(x) = 1/sin(x)
Theorems
Chain Rule
Trigonometric Identities
Suitable Grade Level
Grades 11-12, College Level