derivative of \sqrt[4]{x}-3/x

Lösung

\frac{d}{d x} (4 x - \frac{3}{x})

\frac{x ^{2} + 12 x ^{\frac{3}{4}}}{4 x ^{\frac{11}{4}}}

Schritte zur Lösung

\frac{d}{d x} (4 x - \frac{3}{x})

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

\frac{1}{4 x ^{\frac{3}{4}}} - (- \frac{3}{x ^{2}}) : \frac{x ^{2} + 12 x ^{\frac{3}{4}}}{4 x ^{\frac{11}{4}}}

= \frac{x ^{2} + 12 x ^{\frac{3}{4}}}{4 x ^{\frac{11}{4}}}

\frac{\partial}{\partial x} (ln (x - 2 y))

\frac{\partial}{\partial x} (sin (\frac{x}{y}))

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

\frac{\partial}{\partial x} (2 x^{2} - 3 x y + z - 4)

\int (x^{2} - 6 x + 9) d x