(\partial)/(\partial x)(x^2sin(kx))

Lösung

\frac{\partial}{\partial x} (x^{2} sin (k x))

2 x sin (k x) + cos (k x) k x^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} sin (k x))

Wende die Produktregel an:

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

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (sin (k x)) = cos (k x) k

= 2 x sin (k x) + cos (k x) k x^{2}

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

y^{^{''}} + y^{^{'}} - 2 y = x^{3} - e^{- x}

\frac{d}{d x} (cos (x) + ln (tan (\frac{x}{2})))

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

f (x) = ln (2 x + 1)