derivative (1/(y^2)-3/(y^4))(y+5y^3)

Lösung

ableitung von

(\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 5 y^{3})

\frac{14}{y ^{2}} + \frac{9}{y ^{4}} + 5

Schritte zur Lösung

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 5 y^{3}))

Wende die Produktregel an:

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

f = \frac{1}{y ^{2}} - \frac{3}{y ^{4}}, g = y + 5 y^{3}

= \frac{d}{d y} (\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 5 y^{3}) + \frac{d}{d y} (y + 5 y^{3}) (\frac{1}{y ^{2}} - \frac{3}{y ^{4}})

\frac{d}{d y} (\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) = - \frac{2}{y ^{3}} + \frac{12}{y ^{5}}

\frac{d}{d y} (y + 5 y^{3}) = 1 + 15 y^{2}

= (- \frac{2}{y ^{3}} + \frac{12}{y ^{5}}) (y + 5 y^{3}) + (1 + 15 y^{2}) (\frac{1}{y ^{2}} - \frac{3}{y ^{4}})

Vereinfache

(- \frac{2}{y ^{3}} + \frac{12}{y ^{5}}) (y + 5 y^{3}) + (1 + 15 y^{2}) (\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) : \frac{14}{y ^{2}} + \frac{9}{y ^{4}} + 5

= \frac{14}{y ^{2}} + \frac{9}{y ^{4}} + 5

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

\int_{2}^{x^{3}} t^{4} d t

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 e^{2} t

ma c l a u r in f (x) = e^{8 x}

d er i v a t i v e arctan (x y)