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Beliebt Rechnen >

derivative derivative of ((d^2y(d,x))/((dx^2)))

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Behandle

d

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

Beliebte Beispiele

integral of (sec(θ))

\int (sec (θ)) d θ

derivative of y=csc^2(x)

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

integral 1/((x^{-2))}

in t e g r a l \frac{1}{( x ^{- 2} )}

derivative derivative of sin(2x)

d er i v a t i v e \frac{d}{d x} (sin (2 x))

derivative derivative of 1/((1+x^2))

d er i v a t i v e \frac{d}{d x} (\frac{1}{( 1 + x ^{2} )})