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Questions and Answers
What is the definition of the derivative of a function f(x)?
What is the definition of the derivative of a function f(x)?
- f'(x) = [f(x + h) + f(x)]/h
- f'(x) = [f(x + h) - f(x)]/h
- f'(x) = lim(h → ∞) [f(x + h) - f(x)]/h
- f'(x) = lim(h → 0) [f(x + h) - f(x)]/h (correct)
What is the purpose of differentiation from first principles?
What is the purpose of differentiation from first principles?
- To find the maximum value of a function
- To determine the gradient of a tangent to a curve (correct)
- To find the intersection points of two curves
- To find the area under a curve
What is the meaning of the notation dy/dx?
What is the meaning of the notation dy/dx?
- The quotient of y and x
- y differentiated with respect to x (correct)
- The product of y and x
- x differentiated with respect to y
What is the name given to the symbols D and d/dx?
What is the name given to the symbols D and d/dx?
What is the formula for the gradient of a tangent to a curve at a point x = a?
What is the formula for the gradient of a tangent to a curve at a point x = a?
What is the common notation used to denote the derivative of a function f(x)?
What is the common notation used to denote the derivative of a function f(x)?
Why is the notation dy/dx not considered a fraction?
Why is the notation dy/dx not considered a fraction?
What is the term used to describe the process of finding the derivative of a function?
What is the term used to describe the process of finding the derivative of a function?
What is the purpose of the formula ∂Gradient at a point = lim(h → 0) [f(a + h) - f(a)]/h?
What is the purpose of the formula ∂Gradient at a point = lim(h → 0) [f(a + h) - f(a)]/h?
What is the derivative of a function f(x) written as?
What is the derivative of a function f(x) written as?
What does the notation Dy denote?
What does the notation Dy denote?
What is the term used to describe the process of finding the derivative of a function?
What is the term used to describe the process of finding the derivative of a function?
What is the differential operator denoted by?
What is the differential operator denoted by?
What does the notation dp/dx mean?
What does the notation dp/dx mean?
What is the importance of being consistent in using notations for derivatives?
What is the importance of being consistent in using notations for derivatives?
What is the relationship between the derivative of a function and the gradient of the tangent to the graph?
What is the relationship between the derivative of a function and the gradient of the tangent to the graph?
What is the primary purpose of using the formula for the derivative to determine the gradient of a tangent to a curve?
What is the primary purpose of using the formula for the derivative to determine the gradient of a tangent to a curve?
If we have a function ( f(x) = x^2 ), what is the significance of the notation ( f'(x) )?
If we have a function ( f(x) = x^2 ), what is the significance of the notation ( f'(x) )?
Which of the following notations is NOT a valid way to denote the derivative of a function ( f(x) )?
Which of the following notations is NOT a valid way to denote the derivative of a function ( f(x) )?
What is the relationship between the derivative of a function and the gradient of the tangent to the graph?
What is the relationship between the derivative of a function and the gradient of the tangent to the graph?
What is the purpose of the differential operator ( D ) in the notation ( Df(x) )?
What is the purpose of the differential operator ( D ) in the notation ( Df(x) )?
If we have a function ( f(x) = x^2 ) and we want to find the derivative of the function with respect to ( x ), what is the correct notation to use?
If we have a function ( f(x) = x^2 ) and we want to find the derivative of the function with respect to ( x ), what is the correct notation to use?
What is the significance of the notation ( rac{dy}{dx} ) in the context of differentiation?
What is the significance of the notation ( rac{dy}{dx} ) in the context of differentiation?
Why is it important to be consistent in using notations for derivatives?
Why is it important to be consistent in using notations for derivatives?
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