derivative of (y(x-1)(x^2+1)^{3/2})

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = (x - 1) (x^{2} + 1)^{\frac{3}{2}}

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

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

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

e x p an d \frac{8}{\frac{1}{4}}

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

e x p an d \frac{12 d x}{( x - 8 ) ( x + 3 )}

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

e x p an d ro t a c i o na l (y e^{x y} sin (yz) + 1, - y)