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Derivatives of this function?
Have to find the first and second derivative of this but the subtraction in the exponent is really stumping me on this one:
f(x) = xe^2x-1
3 Answers
- ?Lv 77 years ago
You mention subtraction in the exponent, so I assume that you mean
f(x) = xe^(2x - 1). Just use the chain rule
f'(x) = 2x²e^(2x - 1) + e^(2x - 1) = (2x² + 1)e^(2x - 1). The subtraction does not cause any trouble. Find the second derivative similarly.
- DaveLv 67 years ago
f(x) = xe^2x-1
f ' (x) = e^2x + 2xe^(2x) <--------------------(first derivative)
f '' (x) = 2e^(2x) + 2(f '(x))
f '' (x) = 2e^(2x) + 2[e^2x + 2xe^(2x)]
f '' (x) = 2e^(2x) + 2e^2x + 4xe^(2x)
f '' (x) = 4e^2x + 4xe^(2x) <------------------(second derivative)
