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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e y = cos (x) sin (x)

\int \frac{2}{x ^{2} - 3 x + 2} d x

\frac{\partial}{\partial x} (cos (x + 8 y))

\int_{0}^{l n (2)} \frac{e ^{3 x}}{1 + e ^{6 x}} d x

x \cdot \frac{d y}{d x} + 2 y = 3