(\partial)/(\partial x)(xsin(x^2-y^2))

Lösung

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

sin (x^{2} - y^{2}) + 2 x^{2} cos (x^{2} - y^{2})

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = sin (x^{2} - y^{2})

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (sin (x^{2} - y^{2})) = cos (x^{2} - y^{2}) \cdot 2 x

= 1 \cdot sin (x^{2} - y^{2}) + cos (x^{2} - y^{2}) \cdot 2 xx

Vereinfache

1 \cdot sin (x^{2} - y^{2}) + cos (x^{2} - y^{2}) \cdot 2 xx : sin (x^{2} - y^{2}) + 2 x^{2} cos (x^{2} - y^{2})

= sin (x^{2} - y^{2}) + 2 x^{2} cos (x^{2} - y^{2})

(x + y e^{\frac{y}{x}}) d x - (x e^{\frac{y}{x}}) d y = 0

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

\int e^{2 x} - x e^{2 x} d x

\frac{d}{d x} (- 7 csc (x) + \frac{1}{x ^{5}})

d er i v a t i v e arcsin (\frac{x}{a})