Calculus Answers

Determine the derivative of "y = e" ^cos2"^x"

What is the derivative of ln"( (x^3 - 1) \/ x^2 )"

Determine the derivative of "y = e"^arcsin"^x"

What is the derivative of "y = e"^arcsinx ("1\/ (1+x^2)" )

What is the derivative of "y = arctanx\/ln2x"

Using imlicit differentiation, determine the derivative of "cos(x-2y) = sin(2x+y)"

Using imlicit differentiation, which one of the following is the derivative of

"cos(x-2y) = sin(2x + y)"

Determine the derivative of the function "f(x) = e"^("sqrt(x" ))

Determine the derivative of the function "f(x) = x^2sinx" at "x = \u03c0\/2"

(a) Find fx(x,y), fy(x,y), fx(1,3), and fy(-2,4) for the given function. If 

𝑧 = 𝑓(𝑥, 𝑦) = 3𝑥

ଷ𝑦

ଶ − 𝑥

ଶ𝑦

ଷ + 4𝑥 + 9

(b) A firm estimates that it can sell Q units of its product with an advertising 

expenditure of x thousand dollars where 

𝑄 = 𝑄(𝑥) = −𝑥

ଶ + 600𝑥 + 25

i) Over what level of advertising expenditure is the number of units of 

product sold increasing? 

ii) Over what level of advertising expenditure is the number of units of 

product sold decreasing? 

c) Determine the location and values of the absolute maximum and absolute 

minimum for the given function: 

𝑓(𝑥) = (−𝑥 + 2)

ସ

, 𝑤ℎ𝑒𝑟𝑒 0 ≤ 𝑥 ≤ 3