Chain Rule Homework
Andy Long
Calculus I
pp. 154--, graded #17, 24, and 78

#17: this is a product of two functions which are each compositions: so we’ll use the product rule, and two applications of the special “power” version of the chain rule (see p. 151).

f[x_]:=(2x-3)^4(x^2+x+1)^5
f'[x]
(* just a check, after I simplified: *)
Simplify[%/((2x-3)^3(x^2+x+1)^4)]

#24: this is a quotient of two functions, only the denominator of which is a composition: so we’ll use the quotient rule, andone application of the special “power” version of the chain rule (see p. 151).

f[x_]:=x/Sqrt[7-3x]
Together[f'[x]]

#58:

f[x_]:=Sin[x+Sin[2x]]
f'[x]
Plot[f[x],{x,-2Pi,2Pi}]
Plot[{f[x],f'[x]},{x,-2Pi,2Pi}]

#78: ask yourself 
	what role the various parts of this function are playing; and 
	why the answer makes sense?

L[t_]:=12+2.8 Sin[2Pi(t-80)/365]
L'[t]
L'[80]
L'[141]