derivative of 2\sqrt[5]{(x^3+1^2})

Lösung

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

\frac{12 x ^{2}}{5 ( x ^{3} + 1 ) ^{\frac{3}{5}}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

\frac{1}{5 ( ( x ^{3} + 1 ) ^{2} ) ^{\frac{4}{5}}} \frac{d}{d x} ((x^{3} + 1)^{2})

= \frac{1}{5 ( ( x ^{3} + 1 ) ^{2} ) ^{\frac{4}{5}}} \frac{d}{d x} ((x^{3} + 1)^{2})

\frac{d}{d x} ((x^{3} + 1)^{2}) = 6 x^{2} (x^{3} + 1)

= 2 \cdot \frac{1}{5 ( ( x ^{3} + 1 ) ^{2} ) ^{\frac{4}{5}}} \cdot 6 x^{2} (x^{3} + 1)

Vereinfache

2 \cdot \frac{1}{5 ( ( x ^{3} + 1 ) ^{2} ) ^{\frac{4}{5}}} \cdot 6 x^{2} (x^{3} + 1) : \frac{12 x ^{2}}{5 ( x ^{3} + 1 ) ^{\frac{3}{5}}}

= \frac{12 x ^{2}}{5 ( x ^{3} + 1 ) ^{\frac{3}{5}}}

\frac{\partial}{\partial x} (x^{0.5})

x \to 0 lim (\frac{( 2 + x ) ^{2}}{x})

\int \frac{6}{x ^{3}} + 16 x^{3} d x

\frac{\partial}{\partial t} (e^{t} cos (t))

\int tan^{3} (x) \cdot sec^{3} (x) d x