derivative of 1/12 (x+3^3+(x+3)^{-1})

Lösung

\frac{d}{d x} (\frac{1}{12} (x + 3)^{3} + (x + 3)^{- 1})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{12} (x + 3)^{3} + (x + 3)^{- 1})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{1}{12} (x + 3)^{3}) + \frac{d}{d x} ((x + 3)^{- 1})

\frac{d}{d x} (\frac{1}{12} (x + 3)^{3}) = \frac{( x + 3 ) ^{2}}{4}

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

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

\int_{1}^{4} t ln (\frac{t}{2}) d t

\int \frac{4 x}{1 - 16 x ^{4}} d x

n or ma l y = \frac{x}{a} + \frac{a}{x}, at x = \frac{a}{2}

x \to 5 lim ([x])

t an g e n t f (x) = x^{2} + 8, (- 3, 17)