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

Lösung

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

\int x y x^{2} + y^{2} d y

t an g e n t y = x + \frac{2}{x}

\int_{0}^{4} \frac{x}{2 x + 1} d x

x \to 0 + lim (\frac{5}{x + x ^{2}})

d er i v a t i v e \frac{f ( a + h ) - f ( a - h )}{2 h}