derivative (1/(y^2)-7/(y^4))(y-5y^3)

Lösung

ableitung von

(\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y - 5 y^{3})

\frac{21}{y ^{4}} - \frac{36}{y ^{2}} - 5

Schritte zur Lösung

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{7}{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{7}{y ^{4}}, g = y - 5 y^{3}

= \frac{d}{d y} (\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y - 5 y^{3}) + \frac{d}{d y} (y - 5 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 - 5 y^{3}) = 1 - 15 y^{2}

= (- \frac{2}{y ^{3}} + \frac{28}{y ^{5}}) (y - 5 y^{3}) + (1 - 15 y^{2}) (\frac{1}{y ^{2}} - \frac{7}{y ^{4}})

Vereinfache

(- \frac{2}{y ^{3}} + \frac{28}{y ^{5}}) (y - 5 y^{3}) + (1 - 15 y^{2}) (\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) : \frac{21}{y ^{4}} - \frac{36}{y ^{2}} - 5

= \frac{21}{y ^{4}} - \frac{36}{y ^{2}} - 5

\frac{\partial}{\partial x} (\frac{x + 5}{y + 2})

\int \frac{1}{8 x ^{3}} d x

x \to \infty lim (n 3^{n} + 9^{n})

a re a y = \frac{1}{5} x^{2} - \frac{6}{5} x + \frac{7}{5}, (- 5, 5)

x \to - 1 lim (e^{x - 2})