this is a little overwhelming
where to start?
y= [(e^x + e^pi)*(fourth root (x + 2))] / sqrt(x^2 + 7)
product rule? quotient rule? power rule? chain rule? agh!
It might help if it's in a readable form...
$\displaystyle y = \frac{(e^x + e^\pi)(x + 2)^{\frac{1}{4}}}{(x^2 + 7)^{\frac{1}{2}}}$.
OK, to start, it is a quotient, so start off with the quotient rule.
$\displaystyle \frac{dy}{dx} = \frac{(x^2 + 7)^{\frac{1}{2}}\,\frac{d}{dx}\left[(e^x + e^\pi)(x + 2)^{\frac{1}{4}}\right] - (e^x + e^\pi)(x + 2)^{\frac{1}{4}}\,\frac{d}{dx}\left[(x^2 + 7)^{\frac{1}{2}}\right]}{\left[(x^2 + 7)^{\frac{1}{2}}\right]^2}$.
Can you go from here?