find the derivative and all non zero x-coordinates at which the function gx=x^(a)*(e^(Bx)) has horizontal tagent lines using using product and chain rules and logarithmic differentiation

Question

anonymous · Answer

You have to use both methods mentioned above and the function looks like this:
$$f(x)=x ^{\alpha}e ^{\beta x}$$

anonymous · Answer

$$g(x)=x^ae^{bx}$$
$$g'(x)=ax^{a-1}e^{bx}+x^ae^{bx}\times b$$ by the chain rule

anonymous · Answer

or if you prefer 
$$\large g(x)=\alpha x^{\alpha -1}e^{\beta x}+\beta x^{\alpha}e^{\beta x}$$

anonymous · Answer

factor out the common factor of $e^{\beta x}$ set the rest equal to zero, as $e^{\beta x}$ is never zero

anonymous · Answer

Okay, let me give that a shot!

anonymous · Answer

Um, question? My answer key says the derivative is $$x ^{\alpha -1}e ^{\beta x} (\alpha+\beta x)$$ any idea how they got there?

anonymous · Answer

Hello? Um, help, please?