derivative of (1/(x^2+3)(x^2-1/(x^2)+3))

Lösung

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

6 x + \frac{4}{x ^{5}}

Schritte zur Lösung

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

Vereinfache

(\frac{1}{x ^{2}} + 3) (x^{2} - \frac{1}{x ^{2}} + 3) : 3 x^{2} - \frac{1}{x ^{4}} + 10

= \frac{d}{d x} (3 x^{2} - \frac{1}{x ^{4}} + 10)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (\frac{1}{x ^{4}}) + \frac{d}{d x} (10)

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

\frac{d}{d x} (\frac{1}{x ^{4}}) = - \frac{4}{x ^{5}}

\frac{d}{d x} (10) = 0

= 6 x - (- \frac{4}{x ^{5}}) + 0

Vereinfache

= 6 x + \frac{4}{x ^{5}}

n \to \infty lim (\frac{( - 1 ) ^{n + 1}}{2 n - 1})

\int_{0}^{\frac{π}{2}} sin^{5} (x co) s^{12} x

\frac{\partial}{\partial x} (x^{\frac{1}{2}} \cdot y^{\frac{1}{2}})

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

\frac{\partial}{\partial x} (z^{x^{y}})