derivative (1/(y^2)-7/(y^4))(y-3y^3)

Lösung

ableitung von

(\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y - 3 y^{3})

\frac{21}{y ^{4}} - \frac{22}{y ^{2}} - 3

Schritte zur Lösung

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{7}{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{7}{y ^{4}}, g = y - 3 y^{3}

= \frac{d}{d y} (\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y - 3 y^{3}) + \frac{d}{d y} (y - 3 y^{3}) (\frac{1}{y ^{2}} - \frac{7}{y ^{4}})

\frac{d}{d y} (\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) = - \frac{2}{y ^{3}} + \frac{28}{y ^{5}}

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

= (- \frac{2}{y ^{3}} + \frac{28}{y ^{5}}) (y - 3 y^{3}) + (1 - 9 y^{2}) (\frac{1}{y ^{2}} - \frac{7}{y ^{4}})

Vereinfache

(- \frac{2}{y ^{3}} + \frac{28}{y ^{5}}) (y - 3 y^{3}) + (1 - 9 y^{2}) (\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) : \frac{21}{y ^{4}} - \frac{22}{y ^{2}} - 3

= \frac{21}{y ^{4}} - \frac{22}{y ^{2}} - 3

\frac{\partial}{\partial y} (sin (x + 2 y + 3 z))

\int 2 cos^{3} (3 x) d x

\int_{0}^{\frac{π}{2}} 28 x^{2} sin (x) d x

\frac{d}{d x} (1 - x^{3})

d er i v a t i v e f (x) = (2 x - 5)^{3}