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Beliebt Rechnen >

derivative of x^2y-1

Lösung

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

Lösung

x^{2} \frac{d y}{d x} + 2 x y

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (1) = 0

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

Vereinfache

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

Beliebte Beispiele

tangent y=3x^2+4x,(-2,4)

t an g e n t y = 3 x^{2} + 4 x, (- 2, 4)

(\partial)/(\partial x)(2xy^7+x^8y^7)

\frac{\partial}{\partial x} (2 x y^{7} + x^{8} y^{7})

derivative f(x)=sqrt(x^2+9)

d er i v a t i v e f (x) = x^{2} + 9

derivative y=(((x-2))/((x-3)))^2

d er i v a t i v e y = (\frac{( x - 2 )}{( x - 3 )})^{2}

derivative f(x)=5x+3/x

d er i v a t i v e f (x) = 5 x + \frac{3}{x}