find derivitve of this problem?

Question

y = r^2 / 1+√r

Probably need to use quotient rule?

Answer 1

Yes. The quotient rule would be good ☺

f(x) = g(x)/h(x)
f'(x) = (g'(x)*h(x) - h'(x)*g(x))/(h(x))²


Doug

Answer 2

Quotient rule
dy/dr=(1+sqrt(r))(2r)-(r^2)(1/2(r^-1/2))/(1+sqrt(r))^2
=2r+2r^3/2-1/2(r^3/2)/(1+sqrt(r))^2
=2r+3/2(r^3/2)/(1+sqrt(r))^2

Answer 3

consider, y = r^2/1+√r

taking derivative with respect to r, from both side
and by using quotient rule which is if
y = f1(x)/f2(x) then
dy/dx = [f2(x)*d/dx(f1(x)) - f1(x)*d/dx(f2(x))]/(f2(x))^2
Thus,
dy/dr = [(1+√r)*d/dr(r^2) - r^2*d/dr(1+√r)] / (1+√r)^2
dy/dr = [(1+√r)*(2r) - r^2*(1/2√r)] / (1+√r)^2
by simplifying, we get
dy/dr = [r(2+3/2+√r)] / (1+√r)^2

Answer 4

y=r^2/(1+r^1/2)
y+y*r^1/2=r^2
differentiatig both sides we have
y'+y*1/2*r^-1/2+y'*r^1/2=2r
y'(1+r^1/2)+y/2r^1/2=2r
y'*(1+sqrtr)+y'/2sqrtr=2r
y'[(81+sqrtr)+1/2sqrtr]=2r
y'=2r/{(1+sqrtr)+1/2sqrtr}