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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

\frac{\frac{e ^{\frac{1}{x}}}{x ^{2}} ( 3 + e ^{\frac{1}{x}} ) - ( - \frac{e ^{\frac{1}{x}}}{x ^{2}} ) ( 3 - e ^{\frac{1}{x}} )}{( 3 + e ^{\frac{1}{x}} ) ^{2}} : \frac{6 e ^{\frac{1}{x}}}{x ^{2} ( 3 + e ^{\frac{1}{x}} ) ^{2}}

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

\frac{\partial}{\partial x} (tan (\frac{x y}{z ^{2}}))

\int \frac{x ^{2} - x - 2}{x ^{3} - 2 x - 4} d x

d er i v a t i v e 4 cos^{4} (x)

d er i v a t i v e y = (2 x^{2} + 5) (4 x - 5)

im pl i c i t \frac{d y}{d x}, y = cos (x - y)