#### MATH 3A

##### Final - Practice 1 | General| Grigoryan
If the function is given implicitly by $xe^y - 3y \sin x = 1$, find $y'$ by implicit differentiation.

Sketch the graph of the function $f(x) = \frac{5x}{x^3 - x}$ by first finding:
(a) The domain and asymptotes.
(b) Intervals of monotonicity and concavity.
(c) Local extrema and inflection points.

5. Find the equation of the tangent line to the curve $e^x$ that passes through the origin.