what is the 2nd derivative of this?

Question

2nd derivative of y= 2/(4-x)

Answer 1

f (x) = 2 / (4 - x) = (2) (4 - x)^(- 1)
f `(x) = ( - 2 ) ( 4 - x )^( - 2 ) (- 1)
f `(x) = ( 2) ( 4 - x ) ^( - 2 )
f "(x) = (- 4) (4 - x)^(- 3) (- 1)
f "(x) = (4) / (4 - x) ³

Answer 2

Find the first derivative: y = 2/(x-4)^2
Find the derivative of the derivative a.k.a. the 2nd derivative:
y = -4/(x-4)^3

Answer 3

y = -4/(x-4)^3

Answer 4

f(x)=2(4-x)^(-1)
f'(x)=2(-1)(4-x)^(-2) .(-1)
=2(4-x)^(-2)
f''(x)= 2(-2)(4-x)^(-3) . (-1)
4(4-x)^(-3) = 4/ (4-x)^3

Answer 5

4 / ( (4-x)^3 )

Answer 6

The first derivative is right y' = (1 - x^2) /(1+x^2)^2 y'' = [(1+x^2)^2*(-2x) - (1-x^2)*2(1+x^2)*(2x) ]/(1+x^2)^4 => [-2x(1 + x^4 + 2x^2) - 4x(1 - x^4)] /(1+x^2)^4 =>[-2x - 2x^5 - 4x^3 - 4x + 4x^5] /(1+x^2)^4 =>[2x^5 - 4x^3 - 6x] /(1+x^2)^4 =>2x(x^4 - 2x^2 - 3] /(1+x^2)^4 =>2x[(x^2 - 3)(x^2 +1)]/(1+x^2)^4 =>2x(x^2-3)/(1+x^2)^3

Answer 7

if we introduce Z=x-4

then y=-2/Z

The first derivative is dy/dx=dy/dz*dz/dx=+2/Z² * 1
The second derivative
d²y/dx²=d(dy/dx)/dx= d(dy/dx)/dz*dz/dx

hence the second derivative is equal to -4/Z³ * 1
I replace Z by x-4 and I get

d2y/dz²=-4/(x-4)³

Answer 8

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Answer 9

y= 2 (4-x)^-1
y ' = -2(4-x)^-2 (-1) = 2(4-x)^-2
y ' ' = 4(4-x)^-3 = 4 / (4-x) ³

Answer 10

find the first derivative and then take its derivative