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Beliebt Rechnen >

(\partial)/(\partial x)(x*sin(x^2-y^2))

Lösung

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

Lösung

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})

Beliebte Beispiele

integral from-2 to 2 of 1/(sqrt(|2x|))

\int_{- 2}^{2} \frac{1}{∣ 2 x ∣} d x

integral from-infinity to infinity of 1/(e^x+e^{-x)}

\int_{- \infty}^{\infty} \frac{1}{e ^{x} + e ^{- x}} d x

derivative f(x)=x^{13}

d er i v a t i v e f (x) = x^{13}

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

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

limit as x approaches 2 of 10

x \to 2 lim (10)