Math Problem Statement
Buktikan turunan dari f(x) = sec x adalah f'(x) = sec x tan x.
Solution
The question asks to prove that the derivative of is .
Solution:
Given:
To find , we can use the derivative of with respect to .
Derivative of :
We know:
Proof:
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Rewrite as .
So,
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Use the quotient rule for differentiation: If , then
Here, and .
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Compute and :
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Substitute into the quotient rule:
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Rewrite using trigonometric identities:
Thus, we have shown that
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Related Questions:
- What is the derivative of ?
- How do you prove the derivative of ?
- What is the derivative of ?
- How is the chain rule applied in trigonometric differentiation?
- What is the second derivative of ?
Tip:
Memorizing basic trigonometric derivatives, like those of , , , and , will make solving these kinds of problems faster.
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Trigonometric Functions
Formulas
Derivative of sec x is sec x tan x
Quotient Rule: h'(x) = (u'(x)v(x) - u(x)v'(x)) / [v(x)]^2
Theorems
Quotient Rule
Trigonometric Identities
Suitable Grade Level
Grades 11-12