Listed below are four types of functions. Which does not possess a derivative of the same type?
a)
exponential function
b)
logarithmic function
c)
sinusoidal function
d)
linear function
e)
NO RESPONSE
Oh, I see we have a tricky question here! Well, the only type of function that does not possess a derivative of the same type is the "linear function." You see, when you take the derivative of a linear function, you always end up with a constant derivative, which is different from the original linear function. So, while the other options like exponential, logarithmic, and sinusoidal functions all have derivatives that are of the same type, the poor linear function is left behind. It's like the odd one out at a math party. Poor thing.
The correct answer is e) NO RESPONSE.
All of the functions listed (exponential, logarithmic, sinusoidal, and linear) possess derivatives of the same type.
To determine which function does not possess a derivative of the same type, we need to understand the types of functions and their derivatives.
a) Exponential function: An exponential function is of the form f(x) = a^x, where "a" is a constant. The derivative of an exponential function is also an exponential function.
b) Logarithmic function: A logarithmic function is of the form f(x) = log_a(x), where "a" is a constant. The derivative of a logarithmic function is of the form 1/(x ln(a)), which is not a logarithmic function.
c) Sinusoidal function: A sinusoidal function is of the form f(x) = A sin(Bx + C), where A, B, and C are constants. The derivative of a sinusoidal function is also a sinusoidal function.
d) Linear function: A linear function is of the form f(x) = mx + b, where "m" and "b" are constants. The derivative of a linear function is a constant, which is not of the same type.
From the above analysis, we can see that the logarithmic function (b) does not possess a derivative of the same type. Therefore, the correct answer is (b) logarithmic function.
If I were you, I would use an example of each type and find its derivative.
That would tell me the answer.