(\partial)/(\partial x)(2x^4y+sin(x^4))

Lösung

\frac{\partial}{\partial x} (2 x^{4} y + sin (x^{4}))

8 y x^{3} + cos (x^{4}) \cdot 4 x^{3}

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x^{4} y + sin (x^{4}))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (2 x^{4} y) + \frac{\partial}{\partial x} (sin (x^{4}))

\frac{\partial}{\partial x} (2 x^{4} y) = 8 y x^{3}

\frac{\partial}{\partial x} (sin (x^{4})) = cos (x^{4}) \cdot 4 x^{3}

= 8 y x^{3} + cos (x^{4}) \cdot 4 x^{3}

\int \frac{arcsin ( ln ( x ) )}{x} d x

d er i v a t i v e \frac{1}{cos ( \frac{x}{2} )}

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

d er i v a t i v e (x - 5) (x + 4) (x + 6)

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