F'(x) of F(x)=x(sqrt(5-x))?

Question

I also need to find the f"(x)

Answer 1

since your equation includes the variable x in 2 places, you will need to treat it like 2 equations together.
g(x) = x
h(x) = sqrt(5-x) or (5-x)^(-1/2)
g'(x) = 1
h'(x) = (-1/2)*(5-x)^(-3/2)

F'(x)=g'(x)*h(x) + g(x)*h'(x)

multiply the like terms in the above equation to calc your final answer.

Answer 2

The anti derivative: call sqrt(5-x) = z so -1/2*sqrt(5-x) *x=dz and
dx=-2zdz
also 5-x=z^2 so x= 5 -z^2
so2 (z^2-5)z dz integrated gives you 2(z^4/4-5/2 z^2)+C
substitute for z
f´´(x) = sqrt(5-x) +x( -1/2aqrt(5-x)

Answer 3

Okay, use the power rule here (I assume you know what that is).

So f''(x) = 1/2x(5-x)^-1/2 but if you cant have negative exponents then: x/2(5-x)^1/2 or x/2sqrt(5-x)

Answer 4

Well what is x?