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Questions and Answers
What is the significance of 'المشتقة الأولى' in mathematics?
What is the significance of 'المشتقة الأولى' in mathematics?
- It represents the area under a curve
- It represents the slope of a tangent line
- It represents the rate of change of a function (correct)
- It represents the concavity of a function
How is 'المشتقة الأولى' denoted in calculus notation?
How is 'المشتقة الأولى' denoted in calculus notation?
- f''(x)
- f'(x) (correct)
- ∫f(x)
- Δf(x)
المشتقة الأولى للدالة 3س2
المشتقة الأولى للدالة 3س2
- 6×س (correct)
- س×5
- س
- س+1
Flashcards
What is 'المشتقة الأولى'?
What is 'المشتقة الأولى'?
Represents the rate of change of a function.
Notation for 'المشتقة الأولى'?
Notation for 'المشتقة الأولى'?
f'(x) is the notation for the first derivative of f(x).
What is المشتقة الأولى للدالة 3س2?
What is المشتقة الأولى للدالة 3س2?
The derivative of 3س2 is 6س.
Study Notes
Derivative Concept
- المشتقة الأولى, also known as the first derivative, is a fundamental concept in mathematics that represents the rate of change of a function with respect to one of its variables.
- It is used to measure the instantaneous rate of change of a function at a specific point.
Notation in Calculus
- The first derivative is denoted as f'(x) or (d/dx)f(x) in calculus notation.
Example: Finding the First Derivative
- The first derivative of the function 3x^2 is found by applying the power rule of differentiation, which states that if f(x) = x^n, then f'(x) = nx^(n-1).
- Therefore, the first derivative of 3x^2 is 6x.
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