Mathematics 1 Dersi 6. Ünite Sorularla Öğrenelim
Derivative And İts Applications
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Derivative And İts Applications
What is the product rule?
Let f(x) and g(x) be differentiable at x, then f(x) + g(x), f(x) – g(x), f(x) . g(x) and f(x) /g(x) (Here g(x) ? 0 must be satisfied) are also differentiable and
(f(x) + g(x))’ = f’ (x) + g'(x)
(f(x) – g(x))’ = f ‘ (x) – g'(x)
(f(x) . g(x))’ = f’ (x) . g(x) + f(x) . g'(x)
(The Product Rule)
What is the chain rule?
The Chain Rule: The derivative of composite function f (g(x)) is f'(g(x)) . g’ (x).
What is the constant rule?
From the product rule, it follows that if c ?R is any constant, then
(c . f(x))’ = c . f ‘(x) (The Constant Rule).
What is the equation of the tangent line to the curve y = f(x) at (x0, f(x0))?
The equation of the tangent line to the curve y = f(x) at (x0, f(x0)) is
y–f(x0)=f'(x0)(x–x0)
What is the derivative of a linear function f(x) = ax + b?
It can easily be shown that derivative of a linear function f(x) = ax + b is a, that is (ax+ b)’ = a. For example,
(3x + 5)’ = 3, (–2x – 2)’ = –2.
What does the derivative of a function represent?
The derivative of a function represents the rate of change of a function at a particular point.
What is the product rule?
Let f(x) and g(x) be differentiable at x, then f(x) + g(x), f(x) – g(x), f(x) . g(x) and f(x) /g(x) (Here g(x) ? 0 must be satisfied) are also differentiable and
(f(x) + g(x))’ = f’ (x) + g'(x)
(f(x) – g(x))’ = f ‘ (x) – g'(x)
(f(x) . g(x))’ = f’ (x) . g(x) + f(x) . g'(x)
(The Product Rule)
What is the chain rule?
The Chain Rule: The derivative of composite function f (g(x)) is f'(g(x)) . g’ (x).
What is the constant rule?
From the product rule, it follows that if c ?R is any constant, then
(c . f(x))’ = c . f ‘(x) (The Constant Rule).
What is the equation of the tangent line to the curve y = f(x) at (x0, f(x0))?
The equation of the tangent line to the curve y = f(x) at (x0, f(x0)) is
y–f(x0)=f'(x0)(x–x0)
What is the derivative of a linear function f(x) = ax + b?
It can easily be shown that derivative of a linear function f(x) = ax + b is a, that is (ax+ b)’ = a. For example,
(3x + 5)’ = 3, (–2x – 2)’ = –2.
What does the derivative of a function represent?
The derivative of a function represents the rate of change of a function at a particular point.