derivative of y^2sqrt(9+x^2)

Lösung

\frac{d}{d x} (y^{2} 9 + x^{2})

2 y \frac{d y}{d x} 9 + x^{2} + \frac{x y ^{2}}{9 + x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (y^{2} 9 + x^{2})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y^{2}, g = 9 + x^{2}

= \frac{d}{d x} (y^{2}) 9 + x^{2} + \frac{d}{d x} (9 + x^{2}) y^{2}

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

\frac{d}{d x} (9 + x^{2}) = \frac{x}{9 + x ^{2}}

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

cr i t i c a l f (x) = x^{4} - 4 x^{3} - 2

cr i t i c a l 4 x^{3} - 8

cr i t i c a l x^{\frac{4}{5}} - 2

cr i t i c a l \frac{3 x ^{2}}{( x ^{2} - 4 )}

cr i t i c a l f (x) = - \frac{1}{5}