derivative of (x^6/(12)ln(x)-(x^6)/(72))

Lösung

\frac{d}{d x} (\frac{x ^{6}}{12} ln (x) - \frac{x ^{6}}{72})

\frac{x ^{5} ln ( x )}{2}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{6}}{12} ln (x) - \frac{x ^{6}}{72})

Vereinfache

\frac{x ^{6}}{12} ln (x) - \frac{x ^{6}}{72} : \frac{x ^{6} ln ( x )}{12} - \frac{x ^{6}}{72}

= \frac{d}{d x} (\frac{x ^{6} ln ( x )}{12} - \frac{x ^{6}}{72})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{6} ln ( x )}{12}) - \frac{d}{d x} (\frac{x ^{6}}{72})

\frac{d}{d x} (\frac{x ^{6} ln ( x )}{12}) = \frac{1}{12} (6 x^{5} ln (x) + x^{5})

\frac{d}{d x} (\frac{x ^{6}}{72}) = \frac{x ^{5}}{12}

= \frac{1}{12} (6 x^{5} ln (x) + x^{5}) - \frac{x ^{5}}{12}

Vereinfache

\frac{1}{12} (6 x^{5} ln (x) + x^{5}) - \frac{x ^{5}}{12} : \frac{x ^{5} ln ( x )}{2}

= \frac{x ^{5} ln ( x )}{2}

\frac{d}{d x} (e^{- 5 x} - 5 e^{- 5 x} x)

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

\frac{d}{d x} (\frac{x}{( ∣ y ∣ - ∣ z ∣ )})

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

\int \frac{12}{1 + t ^{2}} d t