Mathematics 1 Dersi 6. Ünite Sorularla Öğrenelim

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.