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

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

Vereinfache

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

y^{^{'}} - \frac{8}{x} y = \frac{y ^{4}}{x ^{18}}

\int X^{2} d X

\frac{\partial}{\partial x} (2 y^{3} + 4 x)

\int \frac{2 - 8 x}{9 - 4 x ^{2}} d x

t an g e n t y = 2 x^{2} - 9 x + 7