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

Lösung

ableitung von

e^{s i n (x)} cos (x)

e^{s i n (x)} cos^{2} (x) - e^{s i n (x)} sin (x)

Schritte zur Lösung

\frac{d}{d x} (e^{s i n (x)} cos (x))

Wende die Produktregel an:

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

f = e^{s i n (x)}, g = cos (x)

= \frac{d}{d x} (e^{s i n (x)}) cos (x) + \frac{d}{d x} (cos (x)) e^{s i n (x)}

\frac{d}{d x} (e^{s i n (x)}) = e^{s i n (x)} cos (x)

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

= e^{s i n (x)} cos (x) cos (x) + (- sin (x)) e^{s i n (x)}

Vereinfache

e^{s i n (x)} cos (x) cos (x) + (- sin (x)) e^{s i n (x)} : e^{s i n (x)} cos^{2} (x) - e^{s i n (x)} sin (x)

= e^{s i n (x)} cos^{2} (x) - e^{s i n (x)} sin (x)

x \to - 1 lim (\frac{x + 1}{6 x ^{2} + 3 + 3 x})

\int 2 x sec^{2} (3 x) d x

\int_{0}^{2} \frac{x}{1 + x ^{2}} d x

\frac{d}{d x} f (x) = 3 x^{2} - 5 x + 2

im pl i c i t \frac{d y}{d x}, x^{5} y + 5 x y^{5} = x + y