derivative y=3x^{-2}-5x^{-3}+3x^{-1}

Lösung

ableitung von

y = 3 x^{- 2} - 5 x^{- 3} + 3 x^{- 1}

- \frac{6}{x ^{3}} + \frac{15}{x ^{4}} - \frac{3}{x ^{2}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (5 x^{- 3}) = - \frac{15}{x ^{4}}

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

= - \frac{6}{x ^{3}} - (- \frac{15}{x ^{4}}) - \frac{3}{x ^{2}}

Vereinfache

= - \frac{6}{x ^{3}} + \frac{15}{x ^{4}} - \frac{3}{x ^{2}}

\frac{\partial}{\partial y} (x tan (y + z))

\int \frac{x ^{4} + 1}{x + 1} d x

\int \frac{1}{( x - 1 ) ( x - 4 )} d x

t an g e n t f (x) = \frac{1}{3 + 2 x}, at x = 2

\int \frac{x ^{2}}{1 + x ^{4}} d x