Determine whether the pair of functions is linearly independent or linearly dependent on the real line. f(x) = e* cos x g(x) = e-* sin x

Consider the function f(x) = v2x + 2. If f -' (x) is the inverse function of f(x), find f -(8). Provide your answer below: f-1(8) =D

Find the derivative of f(z) (z+2)5 z-i

Use the Product Rule to differentiate the function. f(x) = = x° cos(x) f '(x) =

Let ƒ(x) = x/x - 2. Find a function y = g(x) so that (ƒ ∘ g)(x) = x.

Justify whether the function f(z) = ze satisfy the (C-R) equations or not. If it is an analytic function then find f'(z) =ux +ivx

Choose the derivative of sec(x). 1 1+ 22 1 1 1 1 1 1 1+ 22 1

Determine whether the given function is linear or nonlinear. If the function is nonlinear, explain why. [Hint:Recall that a linear function is of the form f (x1; : : : ; xn) = c1x1 + + cnxn where c1; : : : ; cn are constants.](a) f (x; y) = x + 2y(b) g(x1; x2; x3) = cos(x1 + x2 + x3)(c) h(x1; x2; x3; x4) = 6x1 45 x2 + 178 x3 x4(d) k(x1; : : : ; xn) = 3(x1 + + xn 1)(e) f (x1; x2) = x21 x1x2

Let f(x) = 2+ X + 3 e* . Let g be the inverse function of f. Find g'(5).

Let f(x) = In(1 + 7 x). Find f 3(0), that is the third derivative of f evaluated at 0