# \ #
# "As" \ x \ "is the variable of" \ f(x), "I take it that the variable meant in" \ cos \ "is" \ x, "not" \ \theta. "If this is the case, we proceed as follows:" #
# "We are given:" #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad f(x) \ = \ 6 \sqrt{x} + 5 cos( x ). #
# "First rewrite" \ f(x): #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad f(x) \ = \ 6 x^{1/2} + 5 cos( x ). #
# "Now use the Sum Rule, and then the rules for the basic functions" #
# "present there:" #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad f'(x) \ = \ [ 6 x^{1/2} ]' + [ 5 cos( x ) ]' #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad f'(x) \ = \ 6 [ x^{1/2} ]' + 5 [ cos( x ) ]' #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad f'(x) \ = \ 6 [ 1/2 x^{- 1/2} ] + 5 ( -sin( x ) ) #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad f'(x) \ = \ 6 \cdot 1/2 x^{- 1/2} - 5 sin( x ) #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad f'(x) \ = \ 3 x^{- 1/2} - 5 sin( x ). #
# "Now remove the negative exponents, and write the fractional" #
# "exponent as a radical here:" #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad f'(x) \ = \ 3 ( 1/ x^{ 1/2} ) - 5 sin( x ) #
# \qquad \qquad \quad :. \qquad \qquad \qquad f'(x) \ = \ 3 / \sqrt{x} - 5 sin( x ). #
#"This is our answer." #
# \ #
# "Summarizing:" #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad f(x) \ = \ 6 \sqrt{x} + 5 cos( x ). #
# \qquad \qquad \qquad \qquad \qquad \qquad \quad f'(x) \ = \ 3 / \sqrt{x} - 5 sin( x ). #
