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Beliebt Rechnen >

implicit (dy)/(dx),x^{1/2}+y^{1/2}=9

Lösung

implizite ableitung

\frac{d y}{d x}, x^{\frac{1}{2}} + y^{\frac{1}{2}} = 9

Lösung

\frac{d y}{d x} = - (\frac{y}{x})^{\frac{1}{2}}

Schritte zur Lösung

x^{\frac{1}{2}} + y^{\frac{1}{2}} = 9

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

\frac{1}{2 x ^{\frac{1}{2}}} + \frac{\frac{d y}{d x}}{2 y ^{\frac{1}{2}}} = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = - (\frac{y}{x})^{\frac{1}{2}}

\frac{d y}{d x} = - (\frac{y}{x})^{\frac{1}{2}}

Beliebte Beispiele

integral of (arcsin^3(x))/(sqrt(1-x^2))

\int \frac{arcsin ^{3} ( x )}{1 - x ^{2}} d x

integral of t^2+1

\int t^{2} + 1 d t

derivative of sqrt(x-2y)

\frac{d}{d x} (x - 2 y)

tangent f(x)=x^2-2x-8,\at x=-2

t an g e n t f (x) = x^{2} - 2 x - 8, at x = - 2

fläche y=((3x+1))/2 ,y=x^2-2

a re a y = \frac{( 3 x + 1 )}{2}, y = x^{2} - 2