(\partial)/(\partial x)(-e^{cos(x)}sin(x))

Lösung

\frac{\partial}{\partial x} (- e^{c o s (x)} sin (x))

e^{c o s (x)} sin^{2} (x) - e^{c o s (x)} cos (x)

Schritte zur Lösung

\frac{\partial}{\partial x} (- e^{c o s (x)} sin (x))

Entferne die Konstante:

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

= - \frac{\partial}{\partial x} (e^{c o s (x)} sin (x))

Wende die Produktregel an:

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

f = e^{c o s (x)}, g = sin (x)

= - (\frac{\partial}{\partial x} (e^{c o s (x)}) sin (x) + \frac{\partial}{\partial x} (sin (x)) e^{c o s (x)})

\frac{\partial}{\partial x} (e^{c o s (x)}) = - e^{c o s (x)} sin (x)

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

= - ((- e^{c o s (x)} sin (x)) sin (x) + cos (x) e^{c o s (x)})

Vereinfache

- ((- e^{c o s (x)} sin (x)) sin (x) + cos (x) e^{c o s (x)}) : e^{c o s (x)} sin^{2} (x) - e^{c o s (x)} cos (x)

= e^{c o s (x)} sin^{2} (x) - e^{c o s (x)} cos (x)

\frac{d}{d x} (100 x^{0.25} y^{0.75})

\int_{- 1}^{1} (e^{x} - (x^{2} - 2)) d x

\frac{d y}{d x} = \frac{1}{x ln ( 2 )}

d er i v a t i v e 3 e^{2 x^{2}}

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