(d^3)/(dx^3)((y)(3x^2-5))

Lösung

\frac{d ^{3}}{d x ^{3}} ((y) (3 x^{2} - 5))

3 x^{2} \frac{d ^{3} y}{d x ^{3}} + 18 x \frac{d ^{2} y}{d x ^{2}} + 18 \frac{d y}{d x} - 5 \frac{d ^{3} y}{d x ^{3}}

Schritte zur Lösung

\frac{d ^{3}}{d x ^{3}} ((y) (3 x^{2} - 5))

\frac{d}{d x} (y (3 x^{2} - 5)) = \frac{d y}{d x} (3 x^{2} - 5) + 6 x y

= \frac{d ^{2}}{d x ^{2}} (\frac{d y}{d x} (3 x^{2} - 5) + 6 x y)

\frac{d}{d x} (\frac{d y}{d x} (3 x^{2} - 5) + 6 x y) = 3 x^{2} \frac{d ^{2} y}{d x ^{2}} + 12 x \frac{d y}{d x} - 5 \frac{d ^{2} y}{d x ^{2}} + 6 y

= \frac{d}{d x} (3 x^{2} \frac{d ^{2} y}{d x ^{2}} + 12 x \frac{d y}{d x} - 5 \frac{d ^{2} y}{d x ^{2}} + 6 y)

\frac{d}{d x} (3 x^{2} \frac{d ^{2} y}{d x ^{2}} + 12 x \frac{d y}{d x} - 5 \frac{d ^{2} y}{d x ^{2}} + 6 y) = 3 x^{2} \frac{d ^{3} y}{d x ^{3}} + 18 x \frac{d ^{2} y}{d x ^{2}} + 18 \frac{d y}{d x} - 5 \frac{d ^{3} y}{d x ^{3}}

= 3 x^{2} \frac{d ^{3} y}{d x ^{3}} + 18 x \frac{d ^{2} y}{d x ^{2}} + 18 \frac{d y}{d x} - 5 \frac{d ^{3} y}{d x ^{3}}

\frac{d ^{3}}{d x ^{3}} ((y) (x + 3 x))

e x p an d \frac{( m - 2 k + 5 ) ( m - 2 k + 4 )}{( k - 3 ) ( k - 2 )}

e x p an d \frac{e ^{- s} + 4 s - 28}{s ( - 7 + s )}

s im pl i f y (5 - i)^{4}

e x p an d (x + \frac{5}{4})^{2}