Derivative of an Inverse Linear Function
Given the linear function , a researcher determines that its inverse is . The researcher then calculates the derivative of the inverse function to be the constant . Which of the following statements best assesses the researcher’s work?
A
No mistake; for a linear function, the inverse is also linear and its derivative is constant, correctly computed as .
B
The error lies in mistakenly differentiating the original function instead of its inverse.
C
The mistake is that the derivative of the inverse should depend on x and not be constant.
D
The error is in the determination of the inverse function; it should involve an exponentiation rather than a linear expression.
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