erweitern (y'(x)+(1-sec(x))y^2)tan(x)

Lösung

erweitern

(y^{'} (x) + (1 - sec (x)) y^{2}) tan (x)

tan (x) y' (x) + tan (x) y^{2} - tan (x) sec (x) y^{2}

Schritte zur Lösung

(y^{'} (x) + (1 - sec (x)) y^{2}) tan (x)

= tan (x) (y^{^{'}} (x) + (1 - sec (x)) y^{2})

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = tan (x), b = y^{'} (x), c = (1 - sec (x)) y^{2}

= tan (x) y^{^{'}} (x) + tan (x) (1 - sec (x)) y^{2}

Multipliziere aus

tan (x) y^{2} (1 - sec (x)) : tan (x) y^{2} - tan (x) sec (x) y^{2}

= tan (x) y^{'} (x) + tan (x) y^{2} - tan (x) sec (x) y^{2}

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

e x p an d (e^{\frac{jω}{2}} - e^{- \frac{jω}{2}})^{2}

e x p an d cos (x^{2} + 3 y - 1) (2 x + 3 \frac{d y}{d x})

e x p an d \frac{5 x ^{3} + 14 x ^{2} + 23 x + 6}{( s + 3 ) \cdot ( s - 3 ) \cdot ( s + 1 ) ^{2}}

s im pl i f y 1 + \frac{1}{s ( s + 2.2 )}