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(a) Find the slope of the tangent to the...

(a) Find the slope of the tangent to the cube parabola `y = x^(3)` at the point `x=sqrt(3)/(3)`
(b) Write the equations of the tangents to the curve `y = (1)/(1+x^(2))` at the 1 points of its intersection with the hyperbola `y = (1)/(x+1)`
(c) Write the equation of the normal to the parabola `y = x^(2) + 4x + 1` perpendicular to the line joining the origin of coordinates with the vertex of the parabola.
(d) At what angle does the curve `y = e^(x)` intersect the y-axis

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