Question

f(x)=2x√x(x3−4x√x+6), find f′(4).

Answer 1

first you need to find the inverse of the function

Answer 2

how?

Answer 3

first you need let f'(x) = x and where ever x was in the original problem, replace it with y.
x = 2y√y(y3−4y√y+6)

Answer 4

then find for y
then you will substitute x with 4.

Answer 5

well start by simplifying and rewriting in index form

so you have

\[f(x) = 2x (x^4 - 4x^{\frac{5}{2}} + 6x)^{\frac{1}{2}}\]

now to find f'(x) you need the product rule and chain rule...

hope it helps

Answer 6

@mickey4691 The question is asking for the value of the 1st derivative when x = 4,

not the inverse of the function when x is 4.

Answer 7

oh...ooops

Answer 8

ahhh...product rule, and chain rule