d/(d{x)}(({f}(x,y))({x}^2+{y}^2)ln({x}^2+{y}))

Lösung

\frac{d}{d x} ((f (x, y)) (x^{2} + y^{2}) ln (x^{2} + y))

f (x, y) (2 x ln (x^{2} + y) + \frac{2 x + \frac{d}{d x} ( y )}{x ^{2} + y} (x^{2} + y^{2}))

Schritte zur Lösung

\frac{d}{d x} ((f (x, y)) (x^{2} + y^{2}) ln (x^{2} + y))

Entferne die Konstante:

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

= f (x, y) \frac{d}{d x} ((x^{2} + y^{2}) ln (x^{2} + y))

Wende die Produktregel an:

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

f = x^{2} + y^{2}, g = ln (x^{2} + y)

= f (x, y) (\frac{d}{d x} (x^{2} + y^{2}) ln (x^{2} + y) + \frac{d}{d x} (ln (x^{2} + y)) (x^{2} + y^{2}))

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

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

= f (x, y) (2 x ln (x^{2} + y) + \frac{2 x + \frac{d}{d x} ( y )}{x ^{2} + y} (x^{2} + y^{2}))

e x p an d \frac{x + 3}{( x - 5 ) ( x + 2 )}

e x p an d cos (2 t) - cos (2 t) U (t - π)

e x p an d (x - 1) d x

e x p an d \frac{125 ( 2 n + 3 ) ^{2} ( 2 n + 4 ) ^{2}}{4}

e x p an d (2 π - 45)^{2}