Please see the attached file (word problems, inflection, critical points, and derivatives)

14. You run a small furniture business. You sign a deal with a customer to deliver up to 400 chairs, the exact number to be determined by the customer later. The price will be $90 per chair up to 300 chairs, and above 300, the price will be reduced by $0.25 per chair (on the whole order) for every additional chair over 300 ordered. What are the largest and smallest revenues your company can make under this deal?

For each of the functions in problem 4-8, do the following:
(a) find f' and f''
(b) find the critical points of f.
(c) find any inflection points of f.
(d) evaluate f at its critical points and at the endpoints of the given interval. Identify local and global maxima and minima of f in the interval.
(e) graph f.

The solution is a detailed guide on first derivative and second derivative of functions. It also includes an application dealing with the maximum and minimum revenue of a furniture business.

Y= (1 + 1/x)^1/4
Got the 1st derivative to be Y'= 1/4 (1+1/x)^-3/4 * (-1x)^-2
Is that correct?
Now I need the 2nd derivative, I am completely lost on this. Please work out clearly.

1.) compute the derivative of f(x)= arctan (x^2)
2.) compute the derivative of f(x)= ln(x^2/(2+x))
3.) determine an equation for the line tangent to the graph of y= xe^x at the point on the graph were x=2

Let f(x) be a continuous function of one variable.
a) Give the definition of the derivative.
b) Use this definition to find the derivative of f(x)=x^2+2x-5
c) Evaluate f'(2)

The derivative of a continuous function at x is the slope of the tangent line to the curve at x. The attached pdf file develops the idea of a derivativefirst using slopes of secant lines and then introducing and explaining the difference quotient in detail. An example and an explanation are provided for using the limit of the

I need help solving the following problems. Can you explain to me how to solve these problems?
Find the derivative of y = log(2 + sin〖x)〗
Find the derivative of f(x) = sinh2(3x)
Find the derivative of y = x^(x-1)
Find the derivative of y = ln((1+e^x)/(1-e^x ))
Evaluate ∫_0^(π/4)▒tan

Find the directional derivative of the function at a given point P in the direction of the vector V:
f(x,y,z)= square root of xyz P(2,4,2) V=(4,2,-4)
and
f(x,y,z)= z^3 - (x^2)(y) P(1,6,2) V=(3,4,12)