derivative sin(x)e^{cos(x)}

Lösung

ableitung von

sin (x) e^{c o s (x)}

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

\int sin (7 x + 1) d x

\frac{\partial}{\partial y} (e^{- 2 x} cos (4 y))

d er i v a t i v e - \frac{7}{( x - 7 ) ^{2}}

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

d er i v a t i v e 4 x^{2} + 9