Mathematics 1 Deneme Sınavı Sorusu #1357100

Which one can be said true for derivatives?


The derivative of a differentiable function's second derivative can be called the third derivative of the function.

The derivative of a differentiable function can be called the second derivative of the function.

For the identity function f(x) = x, the derivative is x, that is, (x)' = x.

The slope of the secant line to a curve y = f(x) at (x0, f (x0 )) is m = f ' (x0).

A derivative of a constant is equal to that constant.


Yanıt Açıklaması:

If a function y = f(x) is differentiable, its derivative f '(x) is a function of x. If the derivative f '(x) is differentiable, the derivative of f '(x) is called the second derivative of y = f(x) and is denoted by y¨=f ¨(x). The derivative of the second derivative, i.e., f ¨(x) is called the third derivative which is denoted by y'''= f ''' (x). For a constant function f(x) = c the derivative is zero, that is, (c)' = 0. The slope of the tangent line to a curve y = f(x) at (x0, f (x0 )) is m = f ' (x0). For the identity function f(x) = x, the derivative is 1, that is, (x)' = 1. The answer is A.

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