SOLUTION: Find the derivative of the inverse of f(x) by using 1/derivative of f(x). 1. F(x)=(x+3)^.5 This problem does not sound correct to me, but that is the problem, please help. Tha

Question 164194: Find the derivative of the inverse of f(x) by using 1/derivative of f(x).
1. F(x)=(x+3)^.5
This problem does not sound correct to me, but that is the problem, please help.
Thanks
Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
Find the derivative of the inverse of f(x) by using 1/derivative of f(x).
1. F(x)=(x+3)^.5
This isn't right.
lets first find the inverse of f(x) and then find the derivative of it.
y = (x+3)^(1/2)
x = (y+3)^(1/2)
x^2 = y+3
x^2 - 3 = y
so y'= 2x
now lets find the derivative of x and then take 1/y'.
y = (x+3)^(1/2)
y' = (1/2) * (x+3)^(-1/2) * 1 (by the chain rule)
y' = 1/(2(x+3)^(1/2))
1/y' = 2(x+3)^(1/2)
but as you can see 2x does not equal 2(x+3)^(1/2)

RELATED QUESTIONS
Find f'(x) for f(x)=√(1-8x) using the definition of the derivative (answered by stanbon,Edwin McCravy)

Find f'(x), the derivative of f at X, for F(X) = 1/x (answered by stanbon)

Find the derivative of f(x) = e^x + ln (x +1) + x +5 at (0,... (answered by Fombitz)

Using logarithmic differentiation, find the derivative of F(x) = (x^2+5)^(cot2x). Write... (answered by stanbon,robertb)

Using Limits to Calculate a Derivative Use the definition of the derivative to find f... (answered by jim_thompson5910)

Using Limits to Calculate a Derivative Use the definition of the derivative to find... (answered by fractalier)

Using Limits to Calculate a Derivative Use the definition of the derivative to find f... (answered by fractalier)

find the derivative of... (answered by luke94)

HELP!! Can anyone help with the following type of problem?? Using the quotient rule,... (answered by stanbon)