derivative of (tan(x)/(x^2))

Lösung

\frac{d}{d x} (\frac{tan ( x )}{x ^{2}})

\frac{x sec ^{2} ( x ) - 2 tan ( x )}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{tan ( x )}{x ^{2}})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

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

= \frac{sec ^{2} ( x ) x ^{2} - 2 x tan ( x )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{sec ^{2} ( x ) x ^{2} - 2 x tan ( x )}{( x ^{2} ) ^{2}} : \frac{x sec ^{2} ( x ) - 2 tan ( x )}{x ^{3}}

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

t an g e n t f (x) = \frac{4 x}{x + 3}, (1, 1)

\frac{d}{d θ} (cos (θ) - θ sin (θ))

a re a 9 x^{2}, 8 x^{4} - 8 x^{2}

\frac{d y}{d x} + 2 x^{2} = 0

\int \frac{e ^{x}}{e ^{x} + 6} d x