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

Lösung

ableitung von

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

\frac{14}{y ^{2}} + \frac{15}{y ^{4}} + 3

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d y} (\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) = - \frac{2}{y ^{3}} + \frac{20}{y ^{5}}

\frac{d}{d y} (y + 3 y^{3}) = 1 + 9 y^{2}

= (- \frac{2}{y ^{3}} + \frac{20}{y ^{5}}) (y + 3 y^{3}) + (1 + 9 y^{2}) (\frac{1}{y ^{2}} - \frac{5}{y ^{4}})

Vereinfache

(- \frac{2}{y ^{3}} + \frac{20}{y ^{5}}) (y + 3 y^{3}) + (1 + 9 y^{2}) (\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) : \frac{14}{y ^{2}} + \frac{15}{y ^{4}} + 3

= \frac{14}{y ^{2}} + \frac{15}{y ^{4}} + 3

x \to 3 + lim (18 ln (x - 3))

\frac{d}{d x} (e^{5})

\int \frac{tan ( x )}{x} d x

l a pl a ce t r an s f or m e^{- t} t^{2}

\int 2 x 2 - x^{2} d x