derivative (xsec^2(x)-tan(x))/(4x^2)

Lösung

ableitung von

\frac{x sec ^{2} ( x ) - tan ( x )}{4 x ^{2}}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x sec ^{2} ( x ) - tan ( x )}{4 x ^{2}})

Entferne die Konstante:

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

= \frac{1}{4} \frac{d}{d x} (\frac{x sec ^{2} ( x ) - tan ( x )}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( x sec ^{2} ( x ) - tan ( x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x sec ^{2} ( x ) - tan ( x ) )}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{4} \cdot \frac{2 x sec ^{2} ( x ) tan ( x ) x ^{2} - 2 x ( x sec ^{2} ( x ) - tan ( x ) )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{1}{4} \cdot \frac{2 x sec ^{2} ( x ) tan ( x ) x ^{2} - 2 x ( x sec ^{2} ( x ) - tan ( x ) )}{( x ^{2} ) ^{2}} : \frac{x ^{2} sec ^{2} ( x ) tan ( x ) - x sec ^{2} ( x ) + tan ( x )}{2 x ^{3}}

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

\frac{d y}{d x} = 3 x^{2} + 2 x - 7

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

n = 1 \sum \infty n^{- s i n (2)}

(cos^{2} (θ))^{^{'}}

t a y l or \frac{1}{1 - x}