1.Find the derivative of the function and evaluatef'(x)at the given value ofx.

f(x) = ((sqrt (x))+4x)(x^3/2x);x=4

(for this question i'm getting confused on how the square root gets simplified and the rules that are applied. Please provided a detailed explanation.

2.Find the slopemand an equation of the tangent line to the graph of the functionfat the specified point.

f(x) =(1+3x^1/2 )/(2+x^3/2); (1,4/3)

3.Find the point(s) on the graph offwhere the tangent line is horizontal. (If an answer does not exist, enter DNE.)

f(x) = (x²+7)(5x).

smallerx-value (x,y)= ?

largerx-value (x,y)=?

4.At a temperature of 20C, the volumeV(in liters) of 1.33 g of O₂is related to its pressurep(in atmospheres) by the formulaV(p) =1/p

(a) What is the average rate of change ofVwith respect topaspincreases fromp=3

top=4? in L/atm

(b)What is the rate of change toVwith respect topwhenp=3? in L/atm

5.Find the derivative of the function.

f(x) =2x²(x3)