derivative of (1+2y^2/(ysin(x)))

Lösung

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

\frac{2 sin ( x ) y ^{2} \frac{d y}{d x} - sin ( x ) \frac{d y}{d x} - cos ( x ) y - 2 cos ( x ) y ^{3}}{sin ^{2} ( x ) y ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (y sin (x)) = \frac{d y}{d x} sin (x) + cos (x) y

= \frac{4 y \frac{d y}{d x} y sin ( x ) - ( \frac{d y}{d x} sin ( x ) + cos ( x ) y ) ( 1 + 2 y ^{2} )}{( y sin ( x ) ) ^{2}}

Vereinfache

\frac{4 y \frac{d y}{d x} y sin ( x ) - ( \frac{d y}{d x} sin ( x ) + cos ( x ) y ) ( 1 + 2 y ^{2} )}{( y sin ( x ) ) ^{2}} : \frac{2 sin ( x ) y ^{2} \frac{d y}{d x} - sin ( x ) \frac{d y}{d x} - cos ( x ) y - 2 cos ( x ) y ^{3}}{sin ^{2} ( x ) y ^{2}}

= \frac{2 sin ( x ) y ^{2} \frac{d y}{d x} - sin ( x ) \frac{d y}{d x} - cos ( x ) y - 2 cos ( x ) y ^{3}}{sin ^{2} ( x ) y ^{2}}

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

d x + e^{(3 x)} d y = 0

\frac{d}{d x} (e^{c o s (\frac{1}{x})})

\int \frac{6400 x}{16 x ^{2} + 3200} d x

\frac{d y}{d x} (x y + y - 2 x - 2) = ln (x + 1)