derivative of 6x^4sin(x)

Lösung

\frac{d}{d x} (6 x^{4} sin (x))

6 (4 x^{3} sin (x) + cos (x) x^{4})

Schritte zur Lösung

\frac{d}{d x} (6 x^{4} sin (x))

Entferne die Konstante:

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

= 6 \frac{d}{d x} (x^{4} sin (x))

Wende die Produktregel an:

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

f = x^{4}, g = sin (x)

= 6 (\frac{d}{d x} (x^{4}) sin (x) + \frac{d}{d x} (sin (x)) x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (sin (x)) = cos (x)

= 6 (4 x^{3} sin (x) + cos (x) x^{4})

\frac{\partial}{\partial x} (4 x^{2} - 8 x y^{4} + 7 a y^{5} - 3)

t a y l or sin (x + 1)

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

\frac{d y}{d x} = e^{x} y^{2}

d er i v a t i v e y = \frac{2 x + 5}{3 x - 2}